Meshless Method For Two Kinds Of Nonlinear Partial Differential Equations

The element-free Galerkin (EFG) method, which is a meshless method, is based onthe moving least-square approximation for the test and trial functions. A variationalmethod is used to obtain the discrete equations, and the essential boundary conditionsare enforced by the penalty method. In this method, the function over the solutiondomain needs only a set of nodes which does not require element connectivity. Thispaper deals with numerical solution of some partial differential equations which areobtained by the EFG method, and compared with the analytical solution. The erroranalysis is also presented. The main work is as followsFirstly, the basic principle of Moving least-square approximation and theconstruction of shape functions for EFG Method are introduced; Secondly, differentkinds of weight functions are presented; At last, we discuss that the effect of supportdomain can impose a tremendous influence on EFG method.The element free Galerkin method is applied fractional diffusion equation. and themeshless method for time fractional diffusion equation and space fractional diffusionequation is presented, and the corresponding formulae are obtained. The present methodhas large amount of calculation but great precision.The element free Galerkin method is applied to the coupled Schro dinger-KdVequations. The discrete equation is produced from the weak form of variational equation,and then the element free Galerkin method for the coupled Schro dinger-KdV equationsis presented. And the corresponding formulae are obtained.