An efficient robust numerical method for singularly perturbed Burgers’ equation

摘要

In this article, we propose a parameter–uniformly convergent numerical method for viscous Burgers’ equation. In order to find a numerical approximation to Burgers’ equation, we linearize the equation to obtain sequence of linear PDEs. The linear PDEs are solved by a finite difference scheme, which comprises of the backward-difference scheme for the time derivative and upwind finite difference scheme for the spatial derivatives. Layer-adapted nonuniform meshes are invoked at each time level to exhibit layer nature of the solution. The nonuniform meshes are obtained by equidistribution of a positive integrable monitor function, which involves the derivative of the solution. It is shown that the methods converges uniformly with respect to the perturbation parameter. Numerical experiments are carried out to validate the ε-uniform error estimate of O(N−1+Δt).