An efficient Strang splitting technique combined with the multiquadric-radial basis function for the Burgers’ equation

Abstract

In the present paper, two effective numerical schemes depending on a second-order Strang splitting technique are presented to obtain approximate solutions of the one-dimensional Burgers' equation utilizing the collocation technique and approximating directly the solution by multiquadric-radial basis function (MQ-RBF) method. To show the performance of both schemes, we have considered two examples of Burgers' equation. The obtained numerical results are compared with the available exact values and also those of other published methods. Moreover, the computed L 2 and L ∞ error norms have been given. It is found that the presented schemes produce better results as compared to those obtained almost all the schemes present in the literature.

A Meshfree Time-Splitting Approach for the Time-Fractional Burgers’ Equation

“…A linear fnite diference scheme is tailored for the numerical solutions of the generalized timefractional Burgers equation in [14]. In [15,16], the authors used lower-and higher-order classical time-splitting methods to solve Burgers' equation. Te authors of [17] presented three diferent time-splitting algorithms with the convergence and stability analysis for nonlinear timefractional diferential equations.…”

“…Te authors of [17] presented three diferent time-splitting algorithms with the convergence and stability analysis for nonlinear timefractional diferential equations. In [12][13][14][15][16][18][19][20][21][22][23][24][25][26][27], the authors proposed numerical schemes such as fnite diference, fnite elements, spectral methods, and radial basis functions to analyze the numerical solutions of the fractional Burgers'-type equations.…”