Meshfree algorithms based on radial basis functions for numerical simulation and to capture shocks behavior of Burgers’ type problems

Abstract

Purpose

The purpose of this paper is to develop two meshfree algorithms based on multiquadric radial basis functions (RBFs) and differential quadrature (DQ) technique for numerical simulation and to capture the shocks behavior of Burgers’ type problems.

Design/methodology/approach

The algorithms convert the problems into a system of ordinary differential equations which are solved by the Runge–Kutta method.

Findings

Two meshfree algorithms are developed and their stability is discussed. Numerical experiment is done to check the efficiency of the algorithms, and some shock behaviors of the problems are presented. The proposed algorithms are found to be accurate, simple and fast.

Originality/value

The present algorithms LRBF-DQM and GRBF-DQM are based on radial basis functions, which are new for Burgers’ type problems. It is concluded from the numerical experiments that LRBF-DQM is better than GRBF-DQM. The algorithms give better results than available literature.

Citation

Jiwari, R., Kumar, S. and Mittal, R.C. (2019), "Meshfree algorithms based on radial basis functions for numerical simulation and to capture shocks behavior of Burgers’ type problems", Engineering Computations, Vol. 36 No. 4, pp. 1142-1168. https://doi.org/10.1108/EC-04-2018-0189