Parallel Alternating Group Methods For Two Kinds Of Nonlinear Wave Equations

The contents of this dissertation are divided into two chapters.In chapter one, two kinds of parallel alternating group methods for solving Burgers' equation which are changed into diffusion equation first by Hopf-Cole transformation is constructed here. These methods based on Saul'yev type asymmetric difference schemes and Crank-Nicolson scheme are unconditionally stable by analysis . The basic idea of the methods is that the grid points on the same time level are divided into a number of groups , the difference equations of each group can be solved independently, hence these methods with intrinsic parallelism can be used directly on parallel computer. The numerical experiments show that these methods have good stability and accuracy.In chapter two, a group of asymmetric difference schemes to approach the KdV equation is given here.These schemes are based on those for convectional and dispersive terms .Using the schemes and the symmetric Crank-Nicolson type scheme,the parallel alternating difference scheme for solving the KdV equation is constructed.The method is unconditionally stable by analysis of linearization procedure,and can be used directly on the parallel computer.The numerical experiments show that the method has good stability and accuracy.