Method of lines for multi-dimensional coupled viscous Burgers’ equations via nodal Jacobi spectral collocation method

Abstract

This paper deals with the multi-dimensional coupled viscous Burgers’ equations, using the method of lines (MOL). Indeed, the solutions are approximated by their Lagrange interpolation on a set of Jacobi-type nodes. Then, an appropriate differentiation matrix is used to approximate the first and the second partial derivatives with respect to spatial variables. This procedure approximates the original PDE problem with an ODE system for the time variable. Then the resulting ODE is solved with an existing ODE-solver. This MOL approach is implemented for 1D, 2D and 3D coupled viscous Burgers’ equations. The numerical test shows efficient numerical accuracy with fewer nodes in comparison with some previous methods.