On the class of high order time stepping schemes based on Padé approximations for the numerical solution of Burgers’ equation

Numerical solution of Burgers’ equation is presented using finite difference methods in space and positivity preserving Padé approximations in time. A class of high order time stepping schemes is introduced. For practical purposes, first, second, third, and fourth order schemes are constructed. Efficient parallel versions of these schemes are given using a splitting technique of rational functions. Accuracy of the schemes is demonstrated by solving a test problem and comparing numerical results with the exact solution. Time evolution graphs show the physical phenomenon of the problem. Convergence tables are given to verify the theoretical order of convergence.