Mixed Spectral And Pseudospectral Methods For The Out-of-circle Problem Of Fisher's Equation

In this thesis,we mainly study the mixed spectral and pseudospectral method based on shifted generalized Laguerre functions and Fourier functions for solving the Fisher equation outside a disc.Firstly,according to the characteristics of the interval of the equation,we shift the domain from(0,+?)to(1,+?),and obtain the new basis function that we need,and get the relevant approximation results.Then,we derive the errors of the orthogonal projection and the interpolation approximation of the mixed shifted generalized Laguerre functions and Fourier functions.Furthermore,we establish the spectral and pseudospectral schemes for the Fisher equation outside a disc,and prove the stability and convergence of the proposed methods.Finally,numerical results demonstrate the efficiency of this new algorithm.