Simulation of blow-up solutions to the generalized KdV equations by moving collocation methods

Boundary value problems

Zhiqiang Zhou¹  Xiaodan Wu¹ 

[1] School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, P.R. China

关键词: Korteweg-de Vries equations;    moving mesh methods;    dimensional analysis;    blow-up solution;    35Q51;    35Q53;    65N50;    65N35;   

DOI  :  10.1186/s13661-016-0546-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The aim of this paper is to simulate the blow-up solutions to generalized Korteweg-de Vries (KdV) equations. The KdV equations are discretized with the use of a quintic Hermite collocation method based on the moving meshes generated by solving moving mesh partial differential equations (MMPDEs). Theoretical analyses are, respectively, conducted to determine the critical parameters in MMPDEs such that the generated meshes can catch up with the blow-up profiles and to show the effectiveness of the generated moving meshes. Lastly, a variety of examples are implemented to confirm our analysis and show the efficiency of the method.

【 授权许可】

CC BY