A fourth-order numerical scheme for solving the modified Burgers equation

A finite-difference scheme based on fourth-order rational approximants to the matrix exponential term in a two-time level recurrence relation is proposed for the numerical solution of the modified Burgers equation. The resulting nonlinear system, which is analyzed for stability, is solved using an already known modified predictor corrector scheme. The results arising from the experiments are compared with the corresponding ones known from the available literature.