Some HOC-ADI Schemes For Two-Dimensional Ginzburg-Landau Equation

Ginzburg-Landau(GL)equation is an important model to describe the phenomenon of superconduc-tivity,which has abundant physical connotation.Therefore it is important and significant to research the numerical schemes of Ginzburg-Landau equation.In this thesis,we mainly construct several efficient numerical schemes,based on the idea of finite difference,for two-dimensional Ginzburg-Landau equation.In Chapter 1,the research backgrounds and preliminaries are introduced,then we describe the outline and the main work of this thesis.In Chapter 2,we apply the high-order compact and alternating direction implicit(HOC-ADI)scheme to two-dimensional GL equation.Five HOC-ADI schemes with second-order accuracy in time and fourth-order in space are proposed for two-dimensional GL equation.The first and the second schemes both are nonlinear,which need nonlinear iteration.Based on scheme ?,scheme ? is presented in order to avoid nonlinear iteration.With the three-time-level ADI scheme and the method of extrapolation,we separately get the linearied scheme ? and scheme ? which both needn't iteration to solve.In Chapter 3,we present some numerical experiments to testify and to compare the superiority of the numerical schemes we have proposed,at the same time,to verify the convergence of our schemes.We also discuss the influence of the parameters on solution in numerical experiments.