The designing approach of difference schemes by controlling the remainder-effect

In this paper, based on the idea of the ‘modified partial differential equation’, a new designing approach to explicit finite difference schemes for the Burgers equation and PDE is proposed. The approach differs from other constructured methods in such a way that it considers the requests of the numerical dissipation and dispersion coefficients first. This method is much more constructional and directional. The results of numerical tests indicate that the method is quite successful.