The Parallel Computing Of KdV Equation And ZK Equation Based On Group Preserving Scheme

KdV equation and Zakharov-Kuznetsov equation, which could explain many physical phenomena, are very important nonlinear wave equations. Numerical solutions of nonlinear wave equations have been extensively treated as one of the main subjects of mathematical analysis over the past three decades. The parallel algorithm design of group preserving scheme for (1+1)-dimensional KdV equation and (2+1)-dimensional ZK equation is concerned in this thesis.First, the group preserving scheme is used in the calculations of (1+1)-dimensional KdV equation. Then the KdV equation is splited into a conserva-tion law equation and a dispersion equation with the Strang’s operator splitting method. Meanwhile, the group preserving scheme for the conservation law equa-tion and dispersion equation has been obtained. The parallel algorithm for KdV equation is designed and some numerical examples are given.Similarly, the group preserving scheme has been used in the calculations of (2+1)-dimensional ZK equation, and the operator splitting algorithm of the ZK equation based on group preserving scheme is obtained. Then the parallel algo-rithm based on the group preserving scheme for ZK equation has been designed. At last some numerical examples are given, and numerical examples calculationed by multiple processors and the speedup are given also.