Solution Method Research Articles

Performance optimization of a printed circuit heat exchanger for the recuperated gas turbine

To further improve the thermal efficiency of gas turbines, the recuperator needs to be employed and the printed circuit heat exchanger with airfoil fins meets the recuperator's requirements of high heat transfer capacity, low flow resistance, and high reliability. However, the effect of airfoil fin pitches is not clear and the structure optimization method should be developed. In this study, the heat transfer quantity and pressure drop per length of the flue gas in the airfoil channels are numerically investigated under different Reynolds numbers and airfoil fin pitches. The results show that the effect of the airfoil transverse pitch has a great effect on the performance of the flue gas and the heat transfer quantity is increased by 82.39 %–96.08 % when the transverse pitch is decreased from 6.0 mm to 1.2 mm. At the same time, the pressure drop per length is increased to 189.39–842.47 Pa/m. The heat transfer performance is varied not obviously when the airfoil longitudinal pitch is varied from 4 mm to 15 mm. Based on the numerical data, the multiple-objective genetic algorithm combined with the backpropagation neural network is proposed for the performance predictions and optimizations. The corresponding Pareto front is obtained and the technique for order preference by similarity to the ideal solution method is employed to obtain the optimal point. Under the current conditions, the heat transfer quantity of the optimal point is 521.25 kW/m2, which is decreased by 34.5 % compared to the highest value, and the pressure drop per length of the optimal point is 108.45 Pa/m, which is decreased by 85.2 % compared to the highest value.

A new wake superposition model and its application in collision prevention control of tri-riser array system

In the field of offshore oil exploitation, the compact multi-riser arrangement increases the risk of collision and has an adverse impact on production and the marine environment. The solution to this problem involves accurate motion prediction and collision prevention control under the effect of flow field superposition between risers, but there is little research on this related theory. This paper improves the traditional wake shielding effect model and further proposes a wake shielding superposition effect model for the mutual influence between risers, in order to establish a comprehensive accurate motion control model for tri-riser array system. A solution method is introduced for this model, both vibration and collision analysis are conducted for the system. The study revealed that solely augmenting the spacing inadequately mitigates system collisions, and active control is an inevitable choice. Based on this, this paper further designs an active boundary controller that is easy to implement in engineering, to achieve collaborative collision prevention control for three risers, and verifies its stability. Compared with traditional PD control, the proposed control method exhibits significant superiority, which can effectively reduce vibration amplitude, significantly increase dynamic spacing, and thus effectively prevent collisions between risers.

Algorithm for the treatment of boundary conditions in NMM-SPH coupling models: Interface element-wise boundary particle scheme

Large deformation and complex fluid flow interactions, known as the fluid–structure interaction (FSI), are common in geotechnical and coastal projects. To address FSI problems involving crack development, block contact and large movement, a numerical model that utilises smoothed particle hydrodynamics for fluid field spatial discretisation and numerical manifold method for solid block domain solution is proposed in the present study. Specifically, to restore the particle inconsistency near the interface and the overflow issue around the sharp corner in traditional coupled methods, a recommended boundary particle approach is designed to provide full support for particles near the interface, regardless of the interface’s geometry. Moreover, this approach enables the choice of different spatial resolutions tailored to requirements of solid and fluid domains. Six numerical examples were conducted to verify the reliability, accuracy and robustness of the new method. Results showed that relative errors around the sharp corner are lower than those in previous studies. Furthermore, the new model performs well in dealing with the motion of blocks with arbitrary shapes, including large movements, block contacts, crack propagations, and large deformations. Additionally, various inner-variable field evolutions between fluids and solids were visualised, which is beneficial for the prediction of multi-hazard scenario outcomes.

Groundwater pollution equation: Lie’s symmetry analysis and numerical consideration

The current study modeled groundwater pollution through the utilization of the advection–diffusion equation - a versatile differential equation that is capable of modeling a variety of real-life processes. Indeed, various methods of solutions were then proposed to examine the governing model after being transformed, starting with Lie’s symmetry, semi-analytical, and numerical methods, including the explicit and implicit finite difference method and the finite element method. Further, the proposed methods were demonstrated on some test models; featuring forced and unforced scenarios of the forcing function. Analytically, Lie’s symmetry method failed to unswervingly reveal the required solution to the problem; however, with the imposition of certain restrictions, a generalized closed-form solution for the forced model was acquired. This fact indeed triggered the quest for the deployment of more methods. Thus, semi-analytically, the adopted decomposition method swiftly gave the resultant closed-form solutions. Numerically, the efficiency of the sought methods was assessed using the L2−norm and CPU time, upon which the implicit schemes were found to win the race. All-in-all, the beseeched semi-analytical method is highly recommended for such investigation; at the same time advocating the effectiveness of the implicit finite difference schemes on advection–diffusion-related equations.

Atomic Layer Deposition of Cu Catalysts on Gas Diffusion Electrodes for Electrochemical CO2 Reduction

Electrochemical CO2 conversion is gaining attention as an important process for carbon fixation through the use of renewable electricity to address the climate change crisis. Copper is a unique single-element catalyst that can induce C-C coupling reactions to generate high-value-added compounds. The triple phase boundary has been successfully controlled at the catalyst interface using gas diffusion electrodes (GDEs) over the past few years, resulting in high C-C coupling performance. Therefore, methods to engineer the catalyst interface on the 3D structure of GDE are of significant importance. Generally, the catalyst on the GDE is introduced through physical vaper deposition (PVD) using sputtering or E-beam evaporation, or through solution methods such as spray coating and drop-casting of nano-particles. However, the porous and tortuous 3D structure of the GDE often result in limited conformality and difficulty in obtaining a uniform and controlled infiltration of the catalyst into the support structure.In this study, we synthesized Cu catalysts directly onto GDE surfaces using plasma-enhanced atomic layer deposition (PE-ALD), which allowed for precise tuning of the catalyst size and loading at the nanoscale [1]. The synthesized catalysts were confirmed to be polycrystalline Cu nanoparticles using grazing incidence X-ray diffraction. To demonstrate the advantages of the conformal and tunable control of PE-ALD deposition, we deposited the same areal mass loading of Cu catalyst onto the GDE substrates using PVD, and compared the CO2 reduction activity in an H-cell environment. The PE-ALD Cu catalyst showed more than 3 times higher current density than the PVD catalyst at the same electrode potential, a low (~10%) Faradaic efficiency (FE) for the hydrogen evolution reaction (HER), and greater than 75% FE for C-C coupling to form C2+ products including ethylene and ethanol, which is comparable to the highest performances reported to date for metallic Cu catalysts in a H-cell environment. Furthermore, stable operation was observed for a duration of 15 hours, with minimal changes in activity and selectivity. In conclusion, the introduction of catalysts using PE-ALD on GDE electrodes represents a powerful new synthesis method that can increase both C-C coupling performance and selectivity compared to PVD deposition, due to its adjustable Cu nanoparticle size and high conformality. Reference 1) J. D. Lenef, S.Y. Lee, K. M. Fuelling, K. E. Rivera Cruz, A. Prajapati, D. O. D. Cornejo, T. H. Cho, K. Sun, E. Alvarado, T. S. Arthur, C. A. Roberts, C. Hahn, C. C. L. McCrory, N. P. Dasgupta, Nano Lett. 23, 10779-10787 (2023)

Operando and Ex-Situ Studies of Columbite Electrode Materials

Storing and utilising electricity from renewable sources is of growing importance as we move away from our reliance on fossil fuels. Batteries and supercapacitors are becoming ever more present in our day to day lives; in order to improve the next generation of batteries and supercapacitors, we must understand on an atomic scale what happens to electrode materials upon charge and discharge. In order to do this, we must combine structural and electrochemical studies, using techniques which use both different length scales and different timescales. These experiments are known as operando experiments and are a valuable tool in analysing new materials for energy storage.Transition metal niobates of the columbite structure (MNb2O6, M = transition or alkali earth metal) have previously been studied for their photocatalytic and magnetic properties but recently have garnered interest as negative electrode materials for batteries and supercapacitors.1 In this study, a series of columbite materials have been studied using a range of operando and ex-situ techniques. Samples were prepared using both solid-state synthesis2 and solution methods. Ex-situ X-ray diffraction and scanning electron microscopy were used to characterise the columbites prior to electrochemical testing. Operando X-ray absorption spectroscopy and operando Raman studies have been used to probe the changes in oxidation state of the transition metals and local structure upon charge/discharge. References Yang, X. Zhao, F. Liao, Q. Cheng, L. Mao, H. Fa and L. Chen, Sustain. Energy Fuels, 2021, 5, 3039Garía Alvarado, A. Orera, J. Canales-Vázquez, and J. T. S. Irvine, Chem. Mater., 2006, 18, 3827-3834 Figure 1

Implementation of the P1 Radiation Model in a Velocity-Turbulent Frequency-Composition Joint PDF Method

ABSTRACT This research employs a more detailed radiation treatment to improve the accuracy of the velocity-turbulent frequency-composition joint probability density function (PDF) methods in numerical solution of the turbulent non-premixed flames. The radiation heat transfer in the traditional velocity-frequency-composition joint PDF methods has been disregarded or treated simply using an emission-only radiation model, even though radiation is important in the combustion systems. In the present PDF method, radiation is modeled using the P1-approximation and the radiative properties are calculated by the weighted-sum-of-gray-gases (WSGG) model. The results of present method are first validated by solving a laboratory turbulent piloted jet flame and comparing them with the measured data. Then, two constructed large-scale flames are modeled and simulated. Results reveal that reabsorption of emitted radiation increases from 2.98% in a laboratory-scale flame to 56.8% in the scaled-up flame and has a strong effect on the temperature distribution in the scaled-up flame. It is shown that reabsorption of emitted radiation increases the peak temperature on the flame axis by 119 degrees. Furthermore, radiation becomes more significant with the increase of the flame scales, so that the radiation fraction increases from 4.15% in the small-scale flame to 16.6% in the large-scale flame.

(Nanocarbons Division Poster Award, 3rd Place) Investigating the Impact of Reaction and Carbonization Variables on ZIF-67 and Its Energy Storage Properties

Metal-organic frameworks (MOFs), with their exceptional properties such as high surface area, well-defined pores, and diverse chemical functionalities, have garnered widespread attention in scientific and industrial domains [1-2]. Among these, zeolitic imidazolate frameworks (ZIFs), known for their chemical and thermal stability, are extensively explored for applications ranging from catalysis and gas adsorption to electronic devices and sensors.By employing a novel hydrothermal method in aqueous solutions at room temperature, ZIF-67 nanocrystals were successfully synthesized, eliminating the need for toxic organic solvents and reducing overall costs. The resulting materials demonstrated notable efficiency in energy storage. To address the increasing demand for scalable synthesis methods, the study investigated the impact of reaction scale, reaction time, and reaction mixture dilution on the yield, morphology, and molecular structure of ZIF-67. The optimized conditions increased the production yield to 83%, surpassing the reported 75%. The subsequent carbonization process under three different regimes (800 °C, 800 °C with 3h ramp, 900 °C) resulted in materials exhibiting promising energy storage capabilities, with capacitance values reaching 81 F g−1 at a low sweep rate of 5 mV s−1. The carbonization yield showed a decrease with increasing carbonization time and temperature, and capacitance values were influenced by the presence of cobalt in the material.A slightly higher specific surface area of sample C-800 is reflected in the slightly higher capacitance values over all sweep rates indicating that specific surface area plays a role in the behavior of here synthesized materials. Capacitance is invariant at higher sweep rates (above 20mV s-1) which can be an indication that a part of the material surface, at macro- and mesopores, is highly responsive and highly conductive. At lower sweep rates micropores become available, due to prolonged time for ion insertion, which increases the capacitance that is unavailable at higher sweep rates. The highest percentage rise in capacitance is also seen in sample C-800 as its micropore volume, 40% of its total volume, is the highest among the samples investigated.Specifically, considering only the carbon part, the specific capacitance reached 176 F g−1, comparable to literature values for MOF-derived carbons [3]. The study suggests that dissolution of cobalt could enhance the material's capacitance behavior, opening avenues for further improvement in energy storage applications. This transformative approach addresses challenges associated with escalating energy demands and showcases the potential of ZIF-67-derived materials in electrochemical applications.AcknowledgementThis research was supported by the Science Fund of the Republic of Serbia, grant number 7750219, Advanced Conducting Polymer-Based Materials for Electrochemical Energy Conversion and Storage, Sensors and Environmental Protection-AdConPolyMat (IDEAS programme)

(Invited) Enhanced Catalysis of Surface-Activated Metallic WSe2 Nanosheets By Single-Atom Pt for High-Performance Li-O2 Battery

Layered materials, such as TMDCs, exhibit various electronic structures attributed to their polymorphism and can be further modificated at the atomic level through chemical treatments. TMDCs in the metallic phase (1T or 1T’ phase) have gained attention as efficient electrocatalystic materials, due to their exceptional transport properties compared to TMDCs in the semiconducting phase (2H phase). TMDCs with the metallic phase have been prepared by atomic-scale post-treatments, such as an intercalation and single-atom doping. However, the precise role of these post-treatments in the catalytic performance of TMDCs is still ambiguous, as it is uncertain whether the enhanced properties arise from charge transfer kinetics in metallic phase or electrochemical properties induced by the post-treatment.Herein, we present a straightforward approach fabrication for fabricating metallic WSe2 nanosheets, which serve as an excellent support for single-atom Pt doping. The incorporation of single-atom Pt into WSe2 nanosheets was achieved using a simple solution method at room temperature. Extensive measurements were conducted, including XAS, XPS, and XPDF to investigate the local coordination structure of Pt-WSe2. These measurements confirmed the presentce of single-atom Pt doping within WSe2 layers. The introduction of single-atom Pt significantly enhanced the kinetics of the oxygen evolution reaction (OER) and oxygen reduction reaction (ORR), leading to improved performance of Li-O2 batteries. Experimental measurements and DFT calculations provided evidence that the enhanced catalytic abilities of Pt-WSe2 originated from the improved interaction between oxygen and the Se vacancy on basal planes of WSe2. Consequently, the Li-O2 battery incorporating the Pt-WSe2 catalyst exhibited a stable discharge and charge cycle for up to 350 cycles, demonstrating its superior durability.

Analytic analysis of free vibration problem of the plate with a rectangular cutout using symplectic superposition method combined with domain decomposition technique

Plates with rectangular cutouts is widely seen in the field of engineering structures. Therefore, it is crucial to examine analytical solutions for free vibration (FV) of these structures. Despite the existence of approximate/numerical methods, analytical solutions are lacking in the literature. In this study, we employ the symplectic superposition method to effectively analyze the FV problems encountered in plates with rectangular cutouts while integrating the domain decomposition technique. To address the issue of irregular geometry, the rectangular cutout plate is divided into multiple sub-plates. By dividing the problem into multiple sub-problems and solving them separately using variable separation and symplectic eigen expansion, we obtain analytical solutions. Finally, we combine the sub-problem solutions to resolve the initial issue. This solution method can be considered a logical, analytical, and systematic approach as it starts with the fundamental governing equation and is derived without assuming forms of solutions. The study presents a comprehensive set of numerical results that include mode shapes (MSs) and natural frequencies (NFs). The results are rigorously validated using the finite element method (FEM) and relevant literature. The symplectic superposition method demonstrates excellent convergence and precise accuracy, making it suitable for analytically modeling more complex mechanical problems of plates.

Rapid Synthesis and Evaluation of Resveratrol-Piperazine Cocrystals by Ultrasound and Microwave Methods.

Resveratrol-piperazine cocrystals have been obtained by ultrasound (US) and microwave-assisted (MW) techniques, using the solution and slurry-based methods, to study the influence of the synthesis method on the resulting cocrystal properties, and scalability of the processes. The potential of these cocrystals is represented by the unique properties of their components, resveratrol, and piperazine, which could be also used in veterinary practice. Resveratrol has antimicrobial, antiviral and anticarcinogenic properties, while piperazine can be used in the treatment of parasitic infections. The influence of ultrasound and microwave-assisted treatment was studied by varying synthesis parameters such as reaction time, temperature, and US or MW power. The main advantage of using these methods is represented by shorter synthesis time compared to conventional methods, resulting in the direct formation of the cocrystals. All samples were obtained in high purity, above 97%. Cocrystal yield correlated positively with ultrasound reaction time, while temperature was not found to influence the microwave synthesis yield up to 50°C, in the case of solution-based methods. MW and US-assisted solution-based methods lead to yields between 52.9 and 68.1%. In the case of the slurry-based method, a minimum reaction time of 5 min leads to the formation of cocrystals with high purity. The resveratrol-piperazine cocrystal's solubility and in vitro antibacterial activity were also evaluated, showing promising results. Ultrasound and microwave-assisted techniques offer a viable alternative for synthesizing resveratrol-piperazine cocrystals with short reaction times, high yield, and purity, suitable for scalable resveratrol-piperazine cocrystals.

New Insights into ZIF-90 Synthesis.

Zeolitic imidazolate frameworks (ZIFs) are traditionally synthesized using N, N-dimethylformamide (DMF). However, DMF is toxic and hazardous to human health and the environment, hence other alternative solvents need to be considered. Herein, three different solvents like methanol, water and acetone were used to replace DMF and to explore the syntheses of ZIF-90 using a conventional and a microwave-assisted solvothermal method to obtain hydrothermally stable products, which also exhibit an increased water uptake. Pure ZIF-90 was synthesized under ambient pressure at 60 °C for 90 min using the conventional solvothermal method in an acetone-water solution, while under microwave irradiation it was formed in only 5 min at 80 °C. Altering methanol, water and acetone in the reaction mixture significantly affected the structural and water adsorption properties of ZIF-90s, which were monitored via PXRD, TGA, nitrogen and water sorption, and SEM. The highly efficient, less toxic, low-cost and activation-free microwave synthesis resulted in the formation of ZIF-90 nanoparticles that exhibited the highest maximum water adsorption capacity (0.37 g/g) and the best hydrothermal stability between water adsorption at 30 °C and desorption at 100 °C at 12.5 mbar among all the products obtained.

Multi-Criteria Decision-Making Approach for Pre-Synthesis Selection of the Optimal Physicochemical Properties of TiO2 Photocatalytic Nanoparticles for Biomedical and Environmental Applications.

Nanomaterials are widely used in several biomedical and environmental applications, due to their ideal properties. However, the synthetic and characterization procedure requires significant costs and has a negative environmental impact. Various methods are available in order to control the pre-synthesis design of the produced materials, predicting their behavior and minimizing the series of experiments. Multi-Criteria Decision-Making is proposed in this study in order to determine the best combination of the physicochemical parameters and to define the best alternative among fifteen different samples of nanostructured titanium dioxide. In particular, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method was applied to achieve a final ranking of the available alternatives by avoiding several of the trials that would follow testing the biological effect and the photocatalytic degradation of organic pollutants. Thus, this approach helps us to stay environmentally and ethically correct, saving time, money, and energy and also providing an optimization of the nanomaterials that are developed.

A Survey of Aero-Engine Blade Modeling and Dynamic Characteristics Analyses

The rotating blade is a key component of an aero-engine, and its vibration characteristics have an important impact on the performance of the engine and are vital for condition monitoring. This paper reviews the research progress of blade dynamics, including three main aspects: modeling of blades, solution methods, and vibration characteristics. Firstly, three popular structural dynamics models for blades are reviewed, namely lumped-mass model, finite element model, and semi-analytical model. Then, the solution methods for the blade dynamics are comprehensively described. The advantages and limitations of these methods are summarized. In the third part, this review summarizes the properties of the modal and vibration responses of aero-engine blades and discusses the typical forms and mechanisms of blade vibration. Finally, the deficiencies and limitations in the current research on blade modeling and vibration analysis are summarized, and the directions for future efforts are pointed out. The purpose of this review is to provide meaningful insights to researchers and engineers in the field of aero-engine blade modeling and dynamic characteristics analysis.

Dynamic Operations of a Mobile Charging Crowdsourcing Platform

This paper investigates the operation of a novel electric vehicles (EVs) charging service mode, that is, crowdsourced mobile charging service for EVs, whereby a crowdsourcing platform is established to arrange suppliers (crowdsourced chargers) to deliver charging service to customers’ electric vehicles (parked EVs) at low-battery levels. From the platform operator’s perspective, we aim to determine the optimal operation strategies for mobile charging crowdsourcing platforms to achieve specific objectives. A mathematical modeling framework is developed to capture the interactions among supply, demand, and service operations in the crowdsourced mobile charging market. To design an efficient solution method to solve the formulated model, we first analyze the model properties by rigorously proving that a crucial variable set for operating the mobile charging crowdsourcing system includes charging price, commission control, and period-specific aggregate demand control. Besides, we provide both an equivalent condition and a necessary condition for checking the feasibility of these crucial variables. On top of this, we construct a search tree according to the operation periods in a day to solve the optimal operation strategies, wherein a nondominated principle is adopted as an accelerating technique in the searching process. The solution obtained from the proposed solution algorithm is proved to be sufficiently close to the actual global optimal solutions of the formulated model up to the resolution of the discretization scheme adopted. Numerical examples provide evidence verifying the model’s validity and the solution method’s efficiency. Overall, the research outcome of this work can offer service operators structured and valuable guidelines for operating mobile charging crowdsourcing platforms. Funding: This work was supported by the Singapore Ministry of Education [Grant RG124/21]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2023.0126 .

Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions

Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions

A Sustainable Inventory Model with Advertisement Effort for Imperfect Quality Items under Learning in Fuzzy Monsoon Demand

In this paper, we proposed a sustainable inventory model with a learning effect for imperfect quality items under different kinds of fuzzy environments like crisp, general fuzzy, cloudy fuzzy, and monsoon fuzzy. We divided the mathematical model into three parts under the learning effect according to the real-time fuzzy components (crisp, cloudy, and monsoon environments) of the demand rate of the items. We minimized the total inventory cost with respect to cycle length in each environment under the proposed assumptions. The non-linear optimization technique is applied for the algorithm and the solution method to find the decision variable. Finally, we compared the total inventory cost under different fuzzy environments and our finding is that the fuzzy monsoon environment is a more effective fuzzy environment than crisp and cloudy fuzzy environments. We have presented a numerical example for the validation of the proposed model and have shown the impact of the inventory input parameters on the cycle length and total inventory fuzzy cost. The managerial insights and future scope of this proposed study have been shown in the sensitivity analysis and conclusion. The limitations, application, future extension and scope, and social implementation have been shown in this research study.

A multi‐objective sustainable closed‐loop supply chain network problem with hybrid facilities

AbstractA sustainable closed‐loop supply chain network requires conjunctive implementation of reverse logistics in the supply chain, with decisions that consider economic, environmental, and social factors. In real life, the problem needs to be addressed by prioritizing targets or interacting between them to give a range of solutions to the decision maker. In this context, this work proposes a novel multi‐objective sustainable closed‐loop supply chain network problem based on the revised network design model with hybrid recovery centers minimizing (1) the total economic cost, (2) the CO2 emission of vehicles used, and (3) the total obnoxious distance. The latter objective is a novel implementation of the social dimension of a sustainable model. A sensitivity analysis of the multi‐objective model is developed through ANOVA. A dataset of instances was generated to test the model and the solution methods, which are configured with AUGMECON2, a linear programming relaxation implemented to improve the CPU time, and AUGMECON2‐EXTENDED to obtain more solutions to avoid exploring all space of the solution. The results show that an AUGMECON2‐EXTENDED implementation outperforms all the selected performance metrics. These performance metrics include NPS, CPU time, RPOS, QM, and HV. The results show an improvement on average of at least , , , , and , respectively, in those metrics, in comparison to other implementations.

Numerical Solution of Linear Second-Kind Convolution Volterra Integral Equations Using the First-Order Recursive Filters Method

A new numerical method for solving Volterra linear convolution integral equations (CVIEs) of the second kind is presented in this work. This new approach uses first-order infinite impulse response digital filters method (IIRFM). Three convolutive kernels were analyzed, the unit kernel and two singular kernels: the logarithmic and generalized Abel kernels. The IIRFM is based on the combined use of the Laplace transformation, a first-order decomposition, and a bilinear transformation. This approach often leads to simple analytical expressions of the approximate solutions, enabling efficient numerical calculation, even using single-precision floating-point numbers. When compared with the method of homotopic perturbations with Laplace transformation (HPM-L), the IIRFM approach does not present, in linear cases, the convergence difficulties inherent to iterative approaches. Unlike most solution methods based on the Laplace transform, the IIRFM has the dual advantage of not requiring the calculation of the Laplace transform of the source function, and of not requiring the systematic calculation of inverse Laplace transforms.

Numerical solution of fuzzy stochastic Volterra integral equations with constant delay

This paper considers the nonlinear fuzzy stochastic Volterra integral equations with constant delay, which are general and include many fuzzy stochastic integral and differential equations discussed in literature. Since Doob's martingale inequality is no longer applicable to such equations, a new maximum inequality is obtained. Combining with the Picard approximation method, the existence and uniqueness of solutions to nonlinear fuzzy stochastic Volterra integral equations with constant delay are given. Moreover we prove that the solution behaves stably in the case of small changes of initial values, kernels and nonlinearities. We further develop a Euler-Maruyama (EM) scheme and prove the strong convergence of the scheme. It is shown that the strong convergence order of the EM method is 0.5 under Lipschitz condition. Moreover, the strong superconvergence order is 1 if further, the kernel h(t,s) of the stochastic term satisfies h(t,t)=0. Numerical examples demonstrated that the numerical results are consistent with the theoretical research conclusions. Furthermore, the application model of the fuzzy stochastic Volterra integral equation with constant delay in population dynamics is considered, and the exact solution of the numerical example is given in explicit form.