Numerical Solution of a Class of Nonlinear Partial Differential Equations by Using Barycentric Interpolation Collocation Method

Abstract

Partial differential equations (PDEs) are widely used in mechanics, control processes, ecological and economic systems, chemical cycling systems, and epidemiology. Although there are some numerical methods for solving PDEs, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, we give the meshless barycentric interpolation collocation method (MBICM) for solving a class of PDEs. Four numerical experiments are carried out and compared with other methods; the accuracy of the numerical solution obtained by the present method is obviously improved.

Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

“…[35] Ref. [33] shooting bvp4c magnetic parameter relies upon the Lorentz force which provides resistance to the flow. By enhancing the Hartmann number, the well-known Lorentz force increases, due to this reason decline in all the component of velocity is observed in the fluid.…”

“…Maleque [32] examined, with the aid of activation energy, the reactions of exothermic or endothermic on variant convective flows. Hongchun et al [33] presented meshless barycentric interpolation collocation technique for finding the solution of PDEs which are encountered in many physical problems. Zhang et al [34] presented numerical technique for fraction control problems using Chebyshev polynomials.…”

Numerical Solution of a Class of Predator-Prey Systems with Complex Dynamics Characters Based on a Sinc Function Interpolation Collocation Method

“…In general, the exact solution of system (4) cannot be obtained, and the approximate solution must be obtained by numerical calculation. Although many kinds of numerical methods of the nonlinear reaction-diffusion system have been announced, such as finite difference method [14], B-spline method [15], finite element method [16,17], spectral method [18][19][20], the perturbation method and variational iteration method [21,22], barycentric interpolation collocation method [23][24][25][26], and reproducing kernel method [27,28], this paper investigates some nonlinear diffusion predator-prey systems [5,12,13] based on a new interpolation collocation method, and the model (21) is adopted as an example to elucidate the solution process.…”

Numerical Simulation of a Class of Three‐Dimensional Kolmogorov Model with Chaotic Dynamic Behavior by Using Barycentric Interpolation Collocation Method

“…Wang [3,4] gave some algorithms of barycentric Lagrange interpolation collocation method (BLICM). Some authors [3,[5][6][7][8] solved all sorts of equations and showed the BLICM has merits of small operations and high precision (see [3,4,9]). This paper numerically simulates some three-dimensional Kolmogorov models with chaotic dynamic behavior.…”