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The purpose of the method is to develop a numerical method for the solution of nonlinear partial differential equations.

A new numerical approach based on Barycentric Rational interpolation has been used to solve partial differential equations.

A numerical technique based on barycentric rational interpolation has been developed to investigate numerical simulation of the Burgers’ and Fisher’s equations. Barycentric interpolation is basically a variant of well-known Lagrange polynomial interpolation which is very fast and stable. Using semi-discretization for unknown variable and its derivatives in spatial direction by barycentric rational interpolation, we get a system of ordinary differential equations. This system of ordinary differential equation’s has been solved by applying SSP-RK43 method. To check the efficiency of the method, computed numerical results have been compared with those obtained by existing methods. Barycentric method is able to capture solution behavior at small values of kinematic viscosity for Burgers’ equation.

To the best of the authors’ knowledge, the method is developed for the first time and validity is checked by stability and error analysis.

The purpose of this paper is to examine the convergence, offered accuracy and efficiency of the bisectional adaptive frequency sampling (AFS) scheme combined with the Stöer-Bulirsch (SB) algorithm as a tool for supporting frequency-domain method-of-moments (MoM) in broadband electromagnetic (EM) simulations.

The AFS and SB procedures have been interfaced with the MoM code, and then, an extensive parametric study has been carried out to explore the performance of the numerical solution for the test problems of reconstructing frequency responses of the wire radiator and scatterer, respectively, over at least a decade bandwidth.

The results give evidence for the efficiency of the overall approach and its capability of constructing the approximation of multi-resonant responses with sharp resonant peaks from a substantially reduced number of EM samples (data points) compared to that of conventional uniform sampling.

Results of the study offer thorough insight into the performance of the AFS-SB technique, and the data given in this paper may be helpful in selecting the convergence criterion and the tolerance for the AFS-SB algorithm to achieve a possibly economical broadband simulation technique.

The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method.

The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs.

Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method.

The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

The purpose of this paper is to obtain accurate numerical solutions of two-dimensional (2-D) and 3-dimensional (3-D) Klein–Gordon–Schrödinger (KGS) equations.

The use of linear barycentric interpolation differentiation matrices facilitates the computation of numerical solutions both in 2-D and 3-D space within reasonable central processing unit times.

Numerical simulations corroborate the efficiency and accuracy of the proposed method.

Linear barycentric interpolation method is applied to 2-D and 3-D KGS equations for the first time, and good results are obtained.

The aim is to present in this paper an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite interval.

The authors introduce a new orthogonal system of rational functions induced by general Jacobi polynomials with the parameters alpha and beta. It is more flexible in applications. In particular, alpha and beta could be regulated, so that the systems are mutually orthogonal in certain weighted Hilbert spaces.

This approach is applied for solving a non‐linear system two‐point boundary value problem (BVP) on semi‐infinite interval, describing the flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium. The new approach reduces the solution of a problem to the solution of a system of algebraic equations.

The paper presents an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite interval.

This meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate not only the high wavenumber problems, but also the variable wave number problems.

In this paper, the authors developed a meshless collocation method by using barycentric Lagrange interpolation basis function based on the Chebyshev nodes to deduce the scheme for solving the three-dimensional Helmholtz equation. First, the spatial variables and their partial derivatives are treated by interpolation basis functions, and the collocation method is established for solving second order differential equations. Then the differential matrix is employed to simplify the differential equations which is on a given test node. Finally, numerical experiments show the accuracy and effectiveness of the proposed method.

The numerical experiments show the advantages of the present method, such as less number of collocation nodes needed, shorter calculation time, higher precision, smaller error and higher efficiency. What is more, the numerical solutions agree well with the exact solutions.

Compared with finite element method, finite difference method and other traditional numerical methods based on grid solution, meshless method can reduce or eliminate the dependence on grid and make the numerical implementation more flexible.

The Helmholtz equation has a wide application background in many fields, such as physics, mechanics, engineering and so on.

This meshless method is first time applied for solving the 3D Helmholtz equation. What is more the present work not only gives the relationship of interpolation nodes but also the test nodes.

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. These issues in the context of the method of finite spheres are discussed.

The problems of Super resolution are broadly discussed in diverse fields. Rather than the progression toward the super resolution models for real-time images, operating hyperspectral images still remains a challenging problem.

This paper aims to develop the enhanced image super-resolution model using “optimized Non-negative Structured Sparse Representation (NSSR), Adaptive Discrete Wavelet Transform (ADWT), and Optimized Deep Convolutional Neural Network”. Once after converting the HR images into LR images, the NSSR images are generated by the optimized NSSR. Then the ADWT is used for generating the subbands of both NSSR and HRSB images. The residual image with this information is obtained by the optimized Deep CNN. All the improvements on the algorithms are done by the Opposition-based Barnacles Mating Optimization (O-BMO), with the objective of attaining the multi-objective function concerning the “Peak Signal-to-Noise Ratio (PSNR), and Structural similarity (SSIM) index”. Extensive analysis on benchmark hyperspectral image datasets shows that the proposed model achieves superior performance over typical other existing super-resolution models.

From the analysis, the overall analysis of the suggested and the conventional super resolution models relies that the PSNR of the improved O-BMO-(NSSR+DWT+CNN) was 38.8% better than bicubic, 11% better than NSSR, 16.7% better than DWT+CNN, 1.3% better than NSSR+DWT+CNN, and 0.5% better than NSSR+FF-SHO-(DWT+CNN). Hence, it has been confirmed that the developed O-BMO-(NSSR+DWT+CNN) is performing well in converting LR images to HR images.

This paper adopts a latest optimization algorithm called O-BMO with optimized Non-negative Structured Sparse Representation (NSSR), Adaptive Discrete Wavelet Transform (ADWT) and Optimized Deep Convolutional Neural Network for developing the enhanced image super-resolution model. This is the first work that uses O-BMO-based Deep CNN for image super-resolution model enhancement.

The electrical performance of high‐speed integrated circuits and digital networks strongly depends on the behavior of interconnects between various components of these systems. The prediction of such performance can only be achieved by the used of computer‐aided design and simulation tools. The simulation of high‐speed digital circuits has gained a significant role in the past few years since it is critical in the evaluation of noise levels, signal corruption and signal delay in fast switching circuits. This paper explores the various aspects and techniques for transmission line simulation; in particular, two different methods are described: the scattering parameter method and the optimal method.

In this paper, a numerical scheme is provided to predict and approximate the multiple solutions for the problem of heat transfer through a straight rectangular fin with temperature-dependent heat transfer coefficient.

The proposed method is based on the two-point Taylor formula as a special case of the Hermite interpolation technique.

An explicit approximate form of the temperature distribution is computed. The convergence analysis is also discussed. Some results are reported to demonstrate the capability of the method in predicting the multiplicity of the solutions for this problem.

The duality of the solution of the problem can be easily predicted by using the presented method. Furthermore, the computational results confirm the acceptable accuracy of the presented numerical scheme even for estimating the unstable lower solution of the problem.