A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator

Abstract

An efficient technique is proposed to solve the one-dimensional Burgers’ equation based on multiquadric radial basis function (MQ-RBF) for space approximation and a Lie-Group scheme for time integration. The comparisons of the numerical results obtained for different values of kinematic viscosity are made with the exact solutions and the reported results to demonstrate the efficiency and accuracy of the algorithm. It is shown that the numerical solutions concur with existing results and the proposed algorithm is efficient and can be easily implemented.

Keywords

• Burgers’ equation
• meshless method
• multiquadric radial basis function (MQ-RBF)
• Lie-group method