Dual Method Research Articles

Dual global-aware propagation for few-shot learning

• A global-aware sample module (GSM) is proposed to capture the global description of each sample. • A global-aware task module (GTM) is used to obtain the global description across tasks. • A feature fusion module incorporating both global task and global sample information is used for label propagation. Few-shot learning remains a challenging problem because it needs to classify unseen categories with only a few samples as limited supervision. The tasks and samples can be extremely different in various few-shot problems, which makes it even more difficult. Due to the local connectivity in CNN, it can not capture the global description of the samples and the features are not discriminative enough from a global viewpoint. Meanwhile, a sample usually reveals similar features in different tasks, which does not consider the global information of the task and weakens the discrimination of features. To address the above issue, we proposed a Dual Global-Aware method for label Propagation (DGAP) to encode two kinds of global description to enhance the discriminative power of the learned features. On the sample level, the global-aware sample module (GSM) is employed to get the contextual description and enhance the feature representation capability of each sample. On the task level, the global-aware task module (GTM) is used to embed the features in the current task to a more appropriate and discriminative position in the feature space which is task-oriented. In the end, a feature fusion module is adopted to combine the features obtained from both global sample and global task respects. Based on the label propagation method, the proposed DGAP improves the performance approximately 2–5% over the baseline on different benchmarks (mini-Imagenet and tiered-Imagenet) across different structures (Conv4 structure and ResNet12 structure), which reaches the state-of-the-art.

Energy-efficient full-duplex UAV relaying with trajectory optimization and power control in maritime communication environments

This paper solves an energy-efficient optimization problem of a fixed-wing unmanned aerial vehicle (UAV) assisted full-duplex mobile relaying in maritime communication environments. Taking the speed and the acceleration of the UAV and the information-causality constraints into consideration, the energy-efficiency of the system under investigation is maximized by jointly optimizing the UAV's trajectory and the individual transmit power levels of the source and the UAV relay nodes. The optimization problem is non-convex and thus cannot be solved directly. Therefore, it is decoupled into two subproblems. One sub-problem is for the transmit power control at the source and the UAV relay nodes, and the other aims at optimizing the UAV's flight trajectory. By using the Lagrangian dual and Dinkelbach methods, the two sub-problems are solved, leading to an iterative algorithm for the joint design of transmit power control and trajectory optimization. Computer simulations demonstrated that by conducting the proposed algorithm, the flight trajectory of the UAV and the individual transmit power levels of the nodes can be flexibly adjusted according to the system conditions, and the proposed algorithm can achieve significantly higher energy efficiency as compared with the other benchmark schemes.

Dual high frequency square wave injection method for dual winding permanent magnet synchronous motor sensorless control

针对高频方波注入法零低速下永磁同步电机无位置传感器控制存在的高频转矩脉动问题, 提出了一种基于双高频方波注入法的双绕组永磁同步电机无位置传感器控制策略。建立永磁同步电机高频数学模型, 分析得到转矩脉动与注入信号的解析关系。对于同相位表贴式双绕组永磁同步电机, 当第一套绕组注入高频方波时, 依据2套绕组的位置关系, 推导了第二套绕组应当注入方波信号的形式, 使同一时刻产生的高频转矩脉动代数和为零, 以消除高频转矩脉动。提取2套绕组高频信号中包含的转子位置估计误差, 比较得到同一时刻误差最小值, 并使用龙贝格观测器追踪转子位置角, 提高了位置角估计精度。实验结果表明, 该方法能够完全消除高频转矩脉动, 位置角估计误差减小了60%。

Preparation and release of novel frog egg-like microspheres by coaxial electrostatic spray technique

• novel frog egg-like microspheres were prepared by coaxial electrostatic spray process. • The microspheres have a distinct core-shell structure. • The microspheres showed porous structures on the surface and inside after drying. • The microspheres can prolong the release of ME. Novel frog egg-like microspheres, referred to as SA@Ca 2+ /PCL-ME microspheres, were created by coaxial electrostatic spray technique, applying a gel formed by cross-linking sodium alginate (SA) with calcium ions as the shell material and a mixture of methyl eugenol (ME) and polycaprolactone (PCL) solution as the core material in the current study. Using optical microscopy, a uniform spherical shape was observed in the microspheres along with a distinct core-shell structure, while its porous internal and external features were visible in SEM images after drying. Furthermore, ME was released in microspheres for more than 12 weeks due to the dual sustained release method comprising a calcium alginate gel and PCL. During 8 weeks of trapping tests, ME-loaded microspheres were shown to be consistently effective.

An Energy-Efficient SIFT Based Feature Extraction Accelerator for High Frame-Rate Video Applications

Visual feature extraction is a key technology of computer vision for intelligent video processing. Efficient feature extraction is a fundamental problem in computer vision applications. Scale-Invariant Feature Transform (SIFT) is one of the most popular feature extraction algorithms because SIFT features are invariant to image scale and rotation and robust to changes in illumination and noise. However, SIFT is a computationally-intensive and power-hungry algorithm, which needs to be accelerated by efficient hardware design to achieve both high-speed feature extraction and high energy efficiency for many high frame-rate video applications at Artificial-intelligent Internet of Things edges. In this work, an energy-efficient SIFT based feature extraction accelerator is proposed. In the Gaussian pyramid and Differences of Gaussian (DoG) pyramid construction process, three design methods are proposed to reduce power consumption and improve information fidelity: a fast and slow dual clock domain design method with a reconfigurable design strategy is proposed to reduce the computation resources; a partial sum reuse design method is proposed to further reduce the computation resources and the amount of computation; a dynamic padding design method is proposed to solve the problem of information loss at image edges and corners after convolution operation. In the keypoint descriptor generation process, an optimized algorithm using circular region and polar coordinates is proposed to parallelize the main orientation assignment and descriptor generation to achieve high-speed processing, while maintaining a comparable matching accuracy with the state-of-the-art designs. The experiment results show that the proposed SIFT hardware accelerator is able to extract features by up to 162 frames per second ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$640\times 480$ </tex-math></inline-formula> pixels) under 100 MHz, with the power consumption of 364.26 mW and energy efficiency of 2.25 mJ/frame based on 180 nm technology, which is suitable for many high frame-rate AIoT applications including autonomous driving cars and unmanned aerial vehicles.

Using dual mutation particle swarm method to optimize the variable cross-section of a thermoelectric generator based on a comprehensive thermodynamic model

The shape design for a thermoelectric generator (TEG) plays an important role in its performance. In this paper, a hyperbolic function was introduced to design a variable cross-section TEG module to optimize the configuration for maximum power generation and efficiency was sought. A comprehensive thermodynamic model was applied to establish the governing equations for the newly designed TEG module. The mutation particle swarm optimization (MPSO) method was invoked to solve the thermodynamic model. The thermodynamic model's output results include the temperatures at both ends of the TE element, thus making it possible to evaluate the actual performance of the TEG module. The results indicate that both the power generation and efficiency of the hyperbolic TEG are superior to those obtained based on a traditional design. The studies also disclosed that the hyperbolic structure can increase the thermal resistance of the TE couple making it possible to enlarge the temperature difference. This is the main mechanism to improve the performance of a hyperbolic TEG. Besides, the four non-dimensional parameters (shape parameter ( β ), area ratio ( μ ), temperature ratio ( θ ), and resistance ratio ( r x )) related to the geometric structure and working conditions have notable effects on the TEG performance. It is thus worthwhile optimizing the TEG power generation and efficiency in the variable searching space of these parameters. However, differing from the traditional optimization, it is necessary to solve the governing equations in every iteration when searching for an optimal configuration based on the comprehensive model. In order to overcome the challenge, the Dual-MPSO algorithm was used in this research. • MPSO is effective in solving the control equations for a comprehensive TEG model. • Hyperbolic varying TE element is better than constant cross-section. • The effect of the temperature ratio on a TEG's performance is non-monotonic. • The cross-sectional area affects the temperature difference of TE elements. • The hyperbolic TEG performance can be optimized through the Dual-MPSO method.

Model Predictive Torque Control for a Dual Three-phase PMSM Using Modified Dual Virtual Vector Modulation Method

Single voltage vectors applied in the conventional model predictive torque control (MPTC) for multiphase motors do not only suffer from serious torque and stator flux ripples but also cause the large harmonic current. To address the aforementioned challenges, an MPTC using a modified dual virtual vector modulation method is proposed to improve the operational performance of a dual three-phase permanent magnet synchronous motor. Virtual voltage vectors are synthesized as the candidate control set to restrain the harmonic current. A transformation method is introduced to consider both the stator flux and torque in the duty cycle modulation. The torque and stator flux ripples are simultaneously reduced by addressing the limitations of nonuniform units. Furthermore, the null voltage vector is then inserted to expand the modulation range and improve the steady-state performance. Moreover, the sawtooth carrier is adopted to address the challenge of the asymmetric switch sequence caused by the modified modulation. Finally, the experimental results are presented to verify the effectiveness and superiority of the proposed MPTC method.

Research on path planning and scheduling of multi AGVs based on a two-way dual path map

With the development of intralogistics technology in factories, multi-AGV scheduling is still an important problem that needs to be solved by the control system. Aiming at the path planning and scheduling problem of automated guided vehicle (AGV) in the factory loading and unloading work, this paper designs a two-way dual path map construction method suitable for the factory, introduces a two-way different weight map construction method suitable for the right path, and uses “simulated road conditions” algorithm to calculate the shorter path, takes the shortest driving distance as the optimization goal to carry out the task scheduling analyzed possible conflicts and gives corresponding solutions. To verify the correctness of the map construction and algorithm, the multi-AGV simulation is carried out by using a robot operating system (ROS). The results show that the proposed method can realize the stable operation of multi-AGV in the factory environment without conflict and collision.

Energy-Aware Relay Optimization and Power Allocation in Multiple Unmanned Aerial Vehicles Aided Satellite-Aerial-Terrestrial Networks

With the explosive growth of various connected devices and the supported services, the satellite-aerial-terrestrial network (SATN) can fulfill the requirements of the increasing data traffic with enlarged coverage and enhanced capacity. In particular, utilizing multiple unmanned aerial vehicles (UAVs) as relays in the SATN holds great promise for bringing lots of benefits in terms of high flexibility and high reliability. However, due to the limited power of UAVs and the long distance of the aerial-satellite links, how to improve system energy efficiency (EE) is still a challenging issue since existing works mainly paid their attentions to resource while neglecting relay strategy optimization among multiple UAVs. Toward this end, in this article we explore the problem of system EE maximization through jointly optimizing relay selection and power allocation as well as UAV deployment. An iterative algorithm is presented as our solution via alternately leveraging coordinate ascent and Lagrangian dual decomposition methods. Extensive simulation results demonstrate that our devised optimization strategy can significantly improve system EE and obtain the optimal relay selection and power allocation decisions.

Synthesis and Characterization of Urethane Acrylate Resin Based on 1,3-Propanediol for Coating Applications

The significant development of industry and the growing demand for renewable fuels lead to the accumulation of massive amounts of glycerol as a by-product. Scientists have been trying to use this product as a raw material for several years. One of its uses is in the acquirement of 1,3-propanediol (PDO). This work presents studies on the synthesis of two new urethane acrylate resins obtained from 1,3-propanediol and urethane acrylate oligomers containing isocyanate groups in each molecule. The method for obtaining the resins was presented, considering various conditions of synthesis, i.e., the structure of the carbon chain of the oligomer used, the molar ratio of the reactants, or the use of solvents. The reactions were monitored in real time by FTIR until the disappearance of the NCO groups. Then, polymer films were prepared from the obtained products and cured using UV radiation or thermally. The obtained coatings were tested in terms of the photopolymerization kinetics and properties of the cured coatings. Resultantly, the obtained bio-sourced coatings were observed to be characterized by good functional properties and a short curing duration, both with the use of UV radiation-based or thermal curing. These types of resins obtained using a bioproduct can be employed as eco-friendly film-forming products in the coating industry for many applications. In particular, due to their potential for dual curing methods (UV or thermal), these resins can be used on three-dimensional surfaces, i.e., those in which there is a possibility of the insufficient availability of UV radiation.

Molecular characterization of indigenous microbes and its potential as a biological control agent of Fusarium stem rot disease (Fusarium verticillioides) on maize

Fusarium stem rot disease caused by Fusarium verticillioides has become one of the most serious issues confronting Indonesian farmers in recent years. An alternative option for suppressing this disease is to use indigenous microbes as an eco-friendly method to reduce synthetic fungicides. The objective of the research was to identify the molecular characteristics and effectiveness of an indigenous microbial consortium in controlling Fusarium stem rot disease. Identification of indigenous microbes is carried out based on molecular characters using universal primers, namely ITS-1/ITS-4 for fungi and 27F/1492R for bacteria. Nucleotide sequences were analyzed using Bioedit 7.2 version and MEGAX software. In vitro testing was carried out using the dual culture method for indigenous fungi and the disc diffusion method for indigenous bacteria. Meanwhile, in planta testing was conducted by evaluating a consortium of fungi and bacteria to control F. verticillioides in the field using a randomized block design with three replications, followed by a 5% DMRT test. The use of universal primer pairs ITS-1/ITS-4 and 27F/1492R succeeded in amplifying DNA bands of indigenous microbial isolates measuring ±600 bp and ±1465 bp, respectively. S6 and S9 bacterial isolates were identified as Bacillus cereus. JRP 7 and SEDF 6A isolates were identified as Trichoderma asperellum and JRP 10 isolate was identified as Penicillium raperi. All identification resulted in homology of >99%. The in vitro inhibitory reactions of isolates JRP 7, JRP 10, SEDF 6A, S6, and S9 against F. verticillioides were >60%. Disease severity of B6B9C10, B6B9C6, B6B9C7, B9C6C7, B9C7C10, and C6C7C10 treatments significantly proved their ability to control F. verticillioides in the field with a lower percentage of disease severity than positive controls, which are 23.33%, 18.89%, 23.33%., 21.85%, 14.07%, and 15.93%, respectively. The B9C7C10 consortium (S9 + JRP 7 + JRP 10 isolates) containing three species of indigenous microbes, i.e. B. cereus, T. asperellum, and P. raperi is the most effective at controlling F. verticillioides and may be developed for use as biopesticide products.

Bregman Three-Operator Splitting Methods

The paper presents primal–dual proximal splitting methods for convex optimization, in which generalized Bregman distances are used to define the primal and dual proximal update steps. The methods extend the primal and dual Condat–Vũ algorithms and the primal–dual three-operator (PD3O) algorithm. The Bregman extensions of the Condat–Vũ algorithms are derived from the Bregman proximal point method applied to a monotone inclusion problem. Based on this interpretation, a unified framework for the convergence analysis of the two methods is presented. We also introduce a line search procedure for stepsize selection in the Bregman dual Condat–Vũ algorithm applied to equality-constrained problems. Finally, we propose a Bregman extension of PD3O and analyze its convergence.

Effective adsorption of tannic acid by porous dual crosslinked soy protein isolate-alginate hybrid spheres from aqueous solution

Soy protein isolate-alginate hybrid spheres (SPIAHS) were prepared sequentially by using Ca2+ ions and glutaraldehyde as crosslinkers via the dual crosslinking method for tannic acid (TA) adsorption. SPIAHS samples before (SPIAHS-1) and after (SPIAHS-2) glutaraldehyde crosslinking were featured by SEM, FT-IR, XPS, etc. Adsorption performance for TA from aqueous solution by the SPIAHS-2 was explored under various experimental conditions, such as different initial pH, adsorbent dosage, temperature, etc. SPIAHS-2 manifested a maximal adsorption capacity of 1030 mg/g, being greater than most of the previously reported biosorbents. This result could be principally ascribed to the increased specific surface area, robust spheres of lamellar porous network structure, and richness of organic functional groups anchored on the SPIAHS-2 surface after glutaraldehyde crosslinking. Adsorption kinetics and isotherm investigations disclosed that TA adsorption onto SPIAHS-2 can be commendably depicted by the pseudo-second-order kinetic and obeyed single molecule layer adsorption of the Langmuir model. Moreover, the mechanism of TA adsorption was identified by the hydrogen bonding interaction between the oxygen and nitrogen functional groups of SPIAHS-2 and multiple hydroxyl groups of TA. The TA-loaded SPIAHS-2 could be regenerated and used repeatedly with relatively high adsorption capacity, showing great potential in wastewater treatment for TA removal.

Exosomal miR-543 derived from umbilical cord mesenchymal stem cells ameliorates endometrial fibrosis in intrauterine adhesion via downregulating N-cadherin

IntroductionHuman umbilical cord mesenchymal stem cells (UCMSCs) play an important role in repairing the damaged endometrium of intrauterine adhesion (IUA). Meanwhile, exosomes released by UCMSCs can mediate intercellular communication by delivering miRNAs. It has been shown that miR-543 level was reduced in IUA tissues. However, the role of miR-543 in the progression of IUA remains largely unknown. Therefore, we investigated the role of UCMSCs-derived exosomal miR-543 in IUA. MethodsIn this study, human endometrial epithelial cells (hEECs) were treated with TGF-β1 for mimicking endometrial fibrosis in vitro. In addition, the IUA-like mouse model in vivo was established by a dual damage method of curettage and LPS infection. ResultsThe level of miR-543 was markedly reduced in hEECs exposed to TGF-β1 and in endometrium tissues of IUA mice. Additionally, miR-543 could be transferred from UCMSCs to hEECs via exosomes. Meanwhile, exosomal miR-543-derived from UCMSCs significantly reduced the expressions of N-cadherin, α-SMA, fibronectin 1 and elevated the expression of E-cadherin in TGF-β1-treated hEECs. Furthermore, UCMSCs-derived exosomal miR-543 attenuated IUA-induced endometrial fibrosis in vivo, as shown by the decreased N-cadherin, α-SMA and fibronectin 1 protein expressions. DiscussionCollectively, UCMSCs-derived exosomal miR-543 was able to prevent endometrial fibrosis both in vitro and in vivo via downregulating N-cadherin. These results may provide an insight into the clinical treatment for IUA.

Point of care diagnosis of dry eye disease with a sensitive immunoassay for dual biomarker detection

Dry eye disease (DED) is a multifactorial eye disease with few effective methods for clinical diagnosis and treatment. It is the most common eye disease with significant health challenges of the unprecedented aging population. Recent proteomic studies and clinical research have led to the discovery of several biologically relevant biomarkers, with increased levels of Interleukin-6 (IL-6) and decreased levels of lactoferrin being clinically validated in the progression of DED. In this study, a sensitive point of care (POC) DED diagnostic method was developed for targeting dual biomarkers of IL-6 and lactoferrin in the tear samples. A paper-based lateral flow immunoassay (LFIA) was established in a double-antibody sandwich fashion with colloid gold nanoparticles acting as probes. The minimal detection concentrations were 0.1 ng/ml and 10 ng/ml for IL-6 and lactoferrin, respectively. Separated conventional ELISA tests were also performed with data confirming results from the LFIA tests. A trial study was conducted with 20 tear samples from DED patients and healthy controls. All DED tear samples exhibited significantly higher levels of IL-6 and decreased levels of lactoferrin, as compared to the normal controls. A quantitative analysis of LFIA images was carried out using ImageJ software for an accurate data interpretation. This dual biomarker detection method is sensitive and affordable with quick turnaround time. Design of a larger clinical study in the future can further validate this POC assay for early diagnosis as well as patients’ self-management of chronic states of DED.

A dual speckle method for eliminating air distortion in high temperature optical measurement experiments

High-temperature deformation measurements based on optical measurement techniques are important for studying material properties. Due to the existence of temperature gradients between the high-temperature subject and the imaging system, the uneven air density distribution leads to random changes in the refractive index of air along the beam transmission path, which triggers random jitter in the images captured by the imaging system, resulting in large errors in the measured displacement field. In this paper, a dual speckle method is developed for eliminating air distortion in high-temperature experiments. The main experimental setup consists of two cameras, where one camera is focused on the speckles sprayed on the specimen surface that can measure the coupled displacement field, and the other camera is focused on the semipermeable speckles, which can measure the pure displacement caused by the change in the refraction index of air. Then, the true displacement of the tested specimen can be obtained by an arithmetic operation after the calculating point meets the one-to-one relationship. A simplified yet effective test was conducted and verified the feasibility of the method proposed, as the error analysis was analyzed in detail.

Valuation of variable annuities under stochastic volatility and stochastic jump intensity

We present an efficient valuation approach for guaranteed minimum benefits embedded in variable annuity contracts, where the log price follows a jump-diffusion model with stochastic volatilities. In particular, we allow separate Cox-Ingersoll-Ross processes for the underlying volatility and the jump intensity, each correlated with the diffusion term of the spot price. To value the contract under such complex stochastic nature, we rely on the recent advances in the frame dual projection methods with the stochastic process approximated by its expectation. As a byproduct of the transparent analytical expression derived, we derive the associated Greeks that provide a practical basis for risk management. Numerical experiments demonstrate the accuracy and efficiency of the proposed method.

Potential Antimicrobe Producer of Endophytic Bacteria from Yellow Root Plant (Arcangelisia flava (L.)) Originated from Enggano Island.

Exploration studies of endophytic bacteria from Arcangelisia flava (L.) and their potential have not much been conducted. This research aims to explore and characterize the antimicrobial activity of endophytic bacteria in A. flava against pathogenic bacteria. This research consists of several steps including the isolation of bacteria, screening of the antimicrobial activity assay using the dual cross streak method, molecular identification through 16s rDNA analysis, and characterization of bioactive compound production through PKS-NRPS gene detection and GC-MS analysis. There are 29 endophytic bacteria that were successfully isolated from A. flava. The antimicrobial activity showed that there are four potential isolates AKEBG21, AKEBG23, AKEBG25, and AKEBG28 that can inhibit the growth of pathogenic bacteria such as Escherichia coli, Staphylococcus aureus, and Pseudomonas aeruginosa. The 16S rDNA sequence analysis showed that these isolates are identified as Bacillus cereus. These four isolates are identified as able to produce the bioactive compounds through the detection of polyketide synthase (PKS) and nonribosomal peptide synthase (NRPS)-encoding genes. B. cereus AKEBG23 has the highest inhibition against pathogenic bacteria, and according to the GC-MS analysis, five major compounds are allegedly involved in its antimicrobial activity such as butylated hydroxytoluene (BHT), diisooctyl phthalate, E-15-heptadecenal, 1-heneicosanol, and E-14-hexadecenal. This result suggested that B. cereus AKEBG23 as the endophytic bacterium from A. flava has a beneficial role as well as the plant itself. The bacterium produces several bioactive compounds that are allegedly involved in its antimicrobial activity against pathogenic bacteria.

Structural health monitoring of carbon fiber reinforced polymer composite laminates for offshore wind turbine blades based on dual maximum correlation coefficient method

Structural health monitoring (SHM) of offshore wind turbine blades (OWTBs) is critical to the safety of wind turbines, which can avoid catastrophic failures and reduce offshore wind turbine operation and maintenance costs. Combined with the damage imaging algorithm based on the reconstruction algorithm for the probabilistic inspection of defects (RAPID), a Lamb wave baseline-free detection method based on maximum similarity of forward-path is proposed to detect the damage of OWTB carbon fiber-reinforced polymer composite laminates. Damage can introduce nonlinearity into the structure, affecting the correlation of the response signal in the forward path with the original input signal. A new method for calculating the baseline-free damage index (DI) based on the dual maximum correlation coefficient method (DMCCM) is proposed by analyzing the maximum correlation coefficient between the forward path response signal and the original excitation signal. The proposed DMCCM compensates the DI by twice comparing the local maximum correlation coefficients and reducing the errors caused by the interference of the reflected wave to the direct wave and the offset of the peak point when intercepting the response signal. Experimental studies are performed using OWTB composite laminates to validate the proposed method further. The detection results of DMCCM are more reliable, accurate, and require less time than existing methods, which is a very promising baseline-free method for visual SHM of OWTB composite laminates.

A non‐overlapping domain decomposition dual reciprocity method for solving the forward–backward heat equation in two‐dimension

AbstractWe apply a boundary element dual reciprocity method (DRBEM) to the numerical solution of the forward–backward heat equation in a two‐dimensional case. The method is employed for the spatial variable via the fundamental solution of the Laplace equation and the Crank–Nicolson finite difference scheme is utilized to treat the time variable. The physical domain is divided into two non‐overlapping subdomains resulting in two standard forward and backward parabolic equations. The subproblems are then treated by the underlying method assuming a virtual boundary in the interface and starting with an initial approximate solution on this boundary followed by updating the solution by an iterative procedure. In addition, we show that the time discrete scheme is unconditionally stable and convergent using the energy method. Furthermore, some computational aspects will be suggested to efficiently deal with the formulation of the proposed method. Finally, two forward–backward problems, for which the exact solution is available, will be numerically solved for two different domains to demonstrate the efficiency of the proposed approach.