| In this paper, we have given several schemes which have weakly dispersive error for the computation of the nonlinear hyperbolic equations in one and two dimensions. The construction of these schemes is based on the theoretical analysis of the papers[1]and[2].We have computed two model problems of the fluid dynamics in one dimension using Lax-Wendroff's scheme, MacCormack's scheme and the scheme provided in this paper. The numerical results show that our schemes have higher accuracy, and especially the oscilation is not appeared behind a shock. |
