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

• Published in: Engineering computations Vol. 36; no. 4; pp. 1142 - 1168
• Main Authors: Jiwari, Ram, Kumar, Sanjay, Mittal, R.C
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 05.06.2019; Emerald Group Publishing Limited
• Subjects: Accuracy; Algorithms; Approximation; Basis functions; Computer simulation; Differential equations; Meshless methods; Methods; Ordinary differential equations; Partial differential equations; Radial basis function; Runge-Kutta method; Burgers’ problems; Eigen value method; Differential quadrature technique; Global and local radial basis functions; Burgers’ problems and stability
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-04-2018-0189

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.