Residual Power Research Articles

Effective transform-expansions algorithm for solving non-linear fractional multi-pantograph system

<abstract> <p>This study presents a new and attractive analytical approach to treat systems with fractional multi-pantograph equations. We introduce the solution as a rapidly-converging series using the Laplace residual power series technique. This method controls the range of convergence and can be easily programmed to find many terms of the series coefficients by computer software. To show the efficiency and strength of the proposed method, we compare the results obtained in this study with those of the Homotopy analysis method and the residual power series technique. Furthermore, two exciting applications of fractional non-homogeneous pantograph systems are discussed in detail and solved numerically. We also present graphical simulations and analyses of the obtained results. Finally, we conclude that the obtained approximate solutions are very close to the exact solutions with a slight difference.</p> </abstract>

Implementation of Yang residual power series method to solve fractional non-linear systems

<abstract><p>In this study, we implemented the Yang residual power series (YRPS) methodology, a unique analytical treatment method, to estimate the solutions of a non-linear system of fractional partial differential equations. The RPS approach and the Yang transform are togethered in the YRPS method. The suggested approach to handle fractional systems is explained along with its application. With fewer calculations and greater accuracy, the limit idea is used to solve it in Yang space to produce the YRPS solution for the proposed systems. The benefit of the new method is that it requires less computation to get a power series form solution, whose coefficients should be established in a series of algebraic steps. Two attractive initial value problems were used to test the technique's applicability and performance. The behaviour of the approximative solutions is numerically and visually discussed, along with the effect of fraction order $ \varsigma $. It was observed that the proposed method's approximations and exact solutions were completely in good agreement. The YRPS approach results highlight and show that the approach may be utilized to a variety of fractional models of physical processes easily and with analytical efficiency.</p></abstract>

Analysis and analytical simulation for a biophysical fractional diffusive cancer model with virotherapy using the Caputo operator

<abstract> <p>In this paper, a biophysical fractional diffusive cancer model with virotherapy is thoroughly analyzed and analytically simulated. The goal of this biophysical model is to represent both the dynamics of cancer development and the results of virotherapy, which uses viruses to target and destroy cancer cells. The Caputo sense is applied to the fractional derivatives. We look at the governing model's existence and uniqueness. For analytical solutions, the Laplace residual power series approach is used. The study investigates the model's dynamic behavior, shedding light on the development of cancer and the effects of virotherapy. The research advances our knowledge of cancer modeling and treatment options. Numerical simulations show the agreement between the analytical results and the related numerical solutions, proving the usefulness of the analytical solution.</p> </abstract>

Effectiveness of Cimetrol SE 11.16 (Alfacypermethrin 4.65% + Pyriproxyfen 1.86% + Tetramethrin 4.65%) in Aedes aegypti and Blatella germanica control in Cuba

In Cuba, insecticides to control Aedes aegypti mosquito and Blatella germanica cockroach has been frequently used with different formulations, such as emulsifiable concentrates, wettable powders, gels, microencapsulates and suspo-emulsions (SE): the latter is a type of formulation that combines the residuality of a suspension concentrate with the speed of effect of "oil in water" (EW) emulsions. The Cimetrol SE 11.16 formulation is composed of a mixture of two pyrethroid molecules with an insect growth regulator, providing the formulation with great residual power combined with eviction power, due to the mode of action of each one of them. In the following study, we evaluated the effectiveness of Cimetrol SE 11.16 in the control of Ae. aegypti through surface bioassays, and of B. germanica through residual treatment. The residual effect on tile, concrete and wood surfaces was evaluated for 10 weeks and fluctuated from the first weeks (but remained high > 80%). However, mortality on all surfaces remained above 80% until week 6. The highest mortalities occurred in plastic and metal during the 10 weeks (100%). To monitor the cockroach infestation rate, sticky traps (ERADIROACH) were used, which resulted in 95% reduction by the eighth week.

Solutions to nonlinear pseudo hyperbolic partial differential equations with nonlocal conditions by using residual power series method

Solutions to nonlinear pseudo hyperbolic partial differential equations with nonlocal conditions by using residual power series method

A hybrid analytical technique for solving multi-dimensional time-fractional Navier-Stokes system

<abstract> <p>In this research, a hybrid method, entitled the Laplace Residual Power Series technique, is adapted to find series solutions to a time-fractional model of Navier-Stokes equations in the sense of Caputo derivative. We employ the proposed method to construct analytical solutions to the target problem using the idea of the Laplace transform and the residual function with the concept of limit at infinity. A simple modification of the suggested method is presented to deal easily with the nonlinear terms constructed on the properties of the power series. Three interesting examples are solved and compared with the exact solutions to test the reliability, simplicity, and capacity of the presented method of solving systems of fractional partial differential equations. The results indicate that the used technique is a simple approach for solving nonlinear fractional differential equations since it depends only on the residual functions and the concept of the limit at infinity without needing differentiation or other complex computations.</p> </abstract>

Research on SOC estimation of residual power of lithium-ion batteries for electric vehicles based on extended Kalman filtering algorithm

Abstract As the energy carrier of electric vehicles, how to accurately estimate the remaining power (SOC) of the battery is one of the key technologies in the field of electric vehicle design. Effective estimation of SOC can bring accurate continuous mileage information to the driver, theoretically avoid overcharging and discharging the battery, and also protect the driver's driving safety. In the research of SOC estimation method, constructing a suitable battery model is an important means to improve SOC estimation and to improve the prediction accuracy. In order to obtain a higher response accuracy of the model, this paper proposes an electric vehicle SOC model based on the extended Kalman filter algorithm. Based on the actual data of lithium-ion power battery, SOC estimation research is carried out. The research shows that: when the internal temperature of the battery is the same as the ambient temperature, and both are 25 °C, the model is accurate, the terminal voltage difference is small, and the average voltage difference is 9mV respectively; at room temperature, the extended Kalman filter algorithm has a significant effect on the recovery percentage of SOC voltage. The average is over 73%, and the accuracy is high. The extended Kalman algorithm in this paper we use to estimate the SOC current waveform. The simulation results show that the SOC discharge current is 4A, which has high estimation accuracy and strong applicability.

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations’ solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem. Because of the simple implementation, the present technique can be extended to solve other important fractional order problems.

SOLVING THE BOUSSINESQ–BURGERS EQUATIONS USING THE LRPS CHAIN APPROACH

This study aims to solve Boussinesq–Burgers equations mathematically, using the Laplace residual power series (LRPS) chain approach. By combining the series of Taylor equations with the Laplace residual error function, the LRPS method was investigated to obtain a unique analytical solution to the powerful nonlinear system of Boussinesq-Burgers equations according to time. At different times, the approximate solutions obtained by the homozygous perturbation technique and the ideal iterative technique for homozygosity were especially compared with the present results, concluding that this method is more accurate and reliable than the analytical techniques examined by the numerical results, which shows us the accuracy of the results obtained. Finally, the illustrative simulation results were checked graphically using a time procedure and method validity representations.

Constructing Analytical Solutions of the Fractional Riccati Differential Equations Using Laplace Residual Power Series Method

In this article, a hybrid numerical technique combining the Laplace transform and residual power series method is used to construct a series solution of the nonlinear fractional Riccati differential equation in the sense of Caputo fractional derivative. The proposed method is implemented to construct analytical series solutions of the target equation. The method is tested for eminent examples and the obtained results demonstrate the accuracy and efficiency of this technique by comparing it with other numerical methods.

Study on an open fuel cycle of IVG.1M research reactor operating with LEU-fuel

The fuel cycle characteristics of the IVG.1M reactor were studied within the framework of the research reactor conversion program to modernize the IVG.1M reactor. Optimum use of the nuclear fuel and reactor was achieved through routine methods which included partial fuel reloading combined with scheduled maintenance operations. Since, the additional problem in planning the fuel cycle of the IVG.1M reactor was the poisoning of the beryllium parts of the core, reflector, and control system. An assessment of the residual power and composition of spent fuel is necessary for the selection and justification of the technology for its subsequent management. Computational studies were performed using the MCNP6.1 program and the neutronics model of the IVG.1M reactor. The proposed scheme of annual partial fuel reloading allows for maintaining a high reactor reactivity margin, stabilizing it within 2–4 βeff for 20 years, and achieving a burnup of 9.9–10.8 MW × day/kg U in the steady state mode of fuel reloading. Spent fuel immediately after unloading from the reactor can be placed in a transport packaging cask for shipping or safely stored in dry storage at the research reactor site.

A fast deconvolution method for multiple sound source localization based on Hilbert curve

To improve the resolution and efficiency of the multiple sound source localization, a fast deconvolution method based on the Hilbert curve, called CLEAN-VH, is developed in this paper. Firstly, the initial cross-spectral matrix of the measured array signal is decomposed by eigenvalue decomposition, and a new cross-spectral matrix function is constructed using the eigenvalues and eigenvectors. Then, the function is used to update the cross-spectral matrix in the process of deconvolution iteration (CLEAN), and the Hilbert curve is introduced to improve the computational efficiency of the output power in the monitoring area. Finally, the distribution of multiple sound sources can be obtained by superimposing the clean beams and residual power spectrum. The superiority of CLEAN-VH is proved by analyzing the key parameters of the method. The search area optimization based on Hilbert curve greatly alleviates the grid mismatch problem and improves the performance of the proposed method. Through the simulation and experimental comparisons with the other three algorithms, such as CLEAN, FB and CLEAN-SC, the proposed CLEAN-VH achieves high-resolution localization of multiple sound sources, better dynamic range and higher computation efficiency. The proposed method provides another choice for the localization of multiple sound sources.

Efficient and optimized communication in biomedical sensor networks based on bioinspired particle swarm optimization for medical applications.

Healthcare, sports, the military, location monitoring and wireless body networks are emerging as technology of major relevance. As a result of the widespread usage of biomedical sensor networks in medical applications, it is essential that data packets containing vital signs be reliably and effectively supplied to the medical center. Because of its mobility, real-time monitoring, cheap cost, and real-time feedback, it may be used in a broad variety of applications. Effective data transport and a limited energy supply are the main challenges in WBAN. Uses genetic heuristics to enhance routing algorithm efficiency. Low-energy adaptive clustering hierarchy (LEACH) and distributed energy efficiency clustering (DEC) are two kinds of clustering algorithms (DEEC). A clustering-based routing protocol may be optimized using this study's optimization approach so that the network's lifetime can be extended.. The cluster heads (CHs) in sensor nodes are picked with the least amount of overhead grading possible. The cluster is being balanced. Passive clustering based on Bioinspired Particle Swarm Optimization (BPSO) should be used for clustering purposes. Routing messages efficiently means sending them quickly and efficiently without using a lot of bandwidth. Using constraints such as distance and residual power, the optimal path for the cluster may be determined with the help of iterative and heuristic chicken swarm optimization (IHCSO) for short. An evaluation of the packet distribution allocation, capacity, and average end-to-end latency illustrates the practicability of the proposed system in research concerning its efficiency. According to the findings of the research, following the technique that was proposed leads to much better outcomes.

Grape-like CNTs/BaTiO3 nanocatalyst boosted hydraulic-driven piezo-activation of peroxymonosulfate for carbamazepine removal

• Grape-like CNTs/BT nanocomposite catalyst with Ti − C bond was synthesized. • CNTs/BT boosted hydraulic-driven piezo-activation of PMS for CBZ removal. • CNTs/BT-PMS system generated much more ROS than BT-PMS and CNTs-PMS systems with less energy. • CNTs acted as fast electron lanes for accelerating separation of piezoelectric carriers. • Piezoelectric field effectively suppressed destruction of CNTs in PMS system. Both carbon nanotubes (CNTs) and piezoelectric materials can activate peroxymonosulfate (PMS). However, the activation of PMS by CNTs suffers from poor reusability while hydraulic-driven piezo-activation of PMS faces the problem of limited charge separation. To solve the above problems, grape-like CNTs/BaTiO 3 (CNTs/BT) nanocatalyst with a Ti − C bond was prepared. Results indicated that hydraulic-driven CNTs/BT-PMS system offered remarkable carbamazepine removal efficiency (91.93%, 120 min) with satisfactory reusability. The energy consumption of PMS activation by CNTs/BT was only 39.33% and 26.59% of those by CNTs and BT, respectively. Piezoresponse force microscopy and finite element simulation further suggested that these superior performances were mainly responsible for the synergistic effects of CNTs and BT, leading to stronger piezoelectric response with efficient piezo-generated charge separation, which in turn improved the efficiency for producing reactive species. Notably, the built-in piezoelectric field of BT constantly replenished electrons to CNTs and effectively suppressed the destruction of CNTs caused by chemical oxidation. This durable composite might be a promising catalyst for PMS activation with potential utilization of residual hydraulic power during water treatment.

A Reliable Algorithm for Solving System of Multi-Pantograph Equations

In this article, a new series solution of a system of pantograph equations is established using the residual power series method (RPSM). The proposed method produces the solution in terms of a convergent infinite series, requiring no linearization, perturbation or discretization, in some cases it reproduces the exact solutions. We apply the RPSM to solve the multi-pantograph equations, and we show that the outcomes are very accurate. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons to the Laplace decomposition approach are made to verify the efficiency and applicability of the presented method in solving similar problems.

Significance of thermal stress in a convective-radiative annular fin with magnetic field and heat generation: application of DTM and MRPSM

The present paper explains the temperature attribute of a convective-radiative rectangular profiled annular fin with the impact of magnetic field. The effect of thermal radiation, convection, and magnetic field on thermal stress distribution is also studied in this investigation. The governing energy equation representing the steady-state heat conduction, convection, and radiation process is transformed into its dimensionless nonlinear ordinary differential equation (ODE) with corresponding boundary conditions using non-dimensional terms. The obtained ODE is then solved analytically by employing the Pade approximant-differential transform method (DTM) and modified residual power series method (MRPSM). Moreover, the important characteristics of the temperature field, the thermal stress, and the impact of some non-dimensional parameters are inspected graphically, and a physical explanation is provided to aid in comprehension. The significant findings of the investigation reveal that temperature distribution enhances with an increase in the magnitude of the heat generation parameter and thermal conductivity parameter, but it gradually decreases with an increment of convective-conductive parameter, Hartmann number, and radiative-conductive parameter. The thermal stress distribution of the fin varies considerably in the applied magnetic field effect.

Novel Network Structure and its Clustering Scheme Based on Residual Power for Wireless Powered Wireless Sensor Networks

Novel Network Structure and its Clustering Scheme Based on Residual Power for Wireless Powered Wireless Sensor Networks

Analytical Solution of Coupled Hirota–Satsuma and KdV Equations

In this study, we applied the Laplace residual power series method (LRPSM) to expand the solution of the nonlinear time-fractional coupled Hirota–Satsuma and KdV equations in the form of a rapidly convergent series while considering Caputo fractional derivatives. We demonstrate the applicability and accuracy of the proposed method with some examples. The numerical results and the graphical representations reveal that the proposed method performs extremely well in terms of efficiency and simplicity. Therefore, it can be utilized to solve more problems in the field of non-linear fractional differential equations. To show the validity of the proposed method, we present a numerical application, compute two kinds of errors, and sketch figures of the obtained results.

A reliable algorithm for higher order boundary value problems

In this manuscript, extension of residual power series method (RPSM) is proposed for ordinary differential equations with boundary conditions. The extended algorithm is tested against different boundary value problems (BVPs), and results are compared with other schemes to show the reliability of proposed methodology. Analysis reveals that extended approach can easily handle BVPs and provide convergent series solution without discretization, perturbation or linearization. Hence, practically RPSM is better choice for scientists and researchers working in different field of engineering and sciences.

A Reliable Way to Deal with the Coupled Fractional Korteweg-De Vries Equations within the Caputo Operator

The development of numeric-analytic solutions and the construction of fractional order mathematical models for practical issues are of the highest concern in a variety of physics, applied mathematics, and engineering applications. The nonlinear Kersten–Krasil’shchik-coupled Korteweg–de Vries-modified Korteweg–de Vries (KdV-mKdV) system is treated analytically in this paper using a unique method, known as the Laplace residual power series (LRPS) approach to find some approximate solutions. The RPS methodology and the Laplace transform operator are combined in the LRPS method. We provide a detailed introduction to the proposed method for dealing with fractional Kersten–Krasil’shchik-linked KdV-mKdV models. When compared to exact solutions, the approach provides analytical solutions with good accuracy. We demonstrate the effectiveness of the current strategy compared to alternative methods for solving nonlinear equations using an illustrative example. The LRPS technique’s results show and highlight that the method may be used for a variety of time-fractional models of physical processes with simplicity and computing effectiveness.