Numerical Analysis Of Two Kinds Of The Nonlinear Diffusion Equations In Statistical Dynamics

The nonlinear diffusion equations are an important class of mathematical physics equations,and their numerical research has important scientific significance and application value.This dissertation proposes a class of explicit-implicit(E-I)difference method and implicit-explicit(I-E)difference method for two types of the nonlinear diffusion equations in statistical dynamics(the nonlinear Fisher diffusion equation and the nonlinear Huxley diffusion equation).The difference methods consist of an explicit(E)difference method and an implicit(I)difference method.The stability and convergence analysis of the numerical solution of the E-I and I-E methods are given.Theoretical analysis and numerical experiments are performed.It shows that the E-I and I-E methods are unconditionally stable,and both space and time are second-order precision.Compared with the classical Crank-Nicolson(C-N)difference method,the calculation time is saved by nearly 34%,which shows that the E-I difference method and the I-E difference method are effective for solving the nonlinear Fisher diffusion equation.In terms of computational accuracy,compared with the existing Haar wavelet format,it is feasible to solve the nonlinear Huxley diffusion equation by this method.Numerical experiments comprehensively compare and analyze C-N format,Haar wavelet format and E-I format from calculation accuracy and computational efficiency.The results show that the computational efficiency of the E-I difference method is higher than that of the traditional C-N format,and the accuracy is higher than that of the Haar wavelet.In summary,the comprehensive calculation performance of the E-I method is optimal.