On The ADI Methods For Boundary Value Problem Of Second Order Elliptic Equations

Elliptic differential equation is a partial of differential equation. For elliptic equations people study the most is the Laplace equation and Poisson equation, but there are many problems in the real life is not just a Laplace equation and Poisson equation can describe.So,this paper studied the elliptic equations with general numerical method for solving the value problem of first side. First of all, using the Taylor to discrete equation, five-point difference scheme, elliptic equation is obtained for the first boundary conditions using directly the discrete transfer method. Then by Richardson iterative formula, an iterative formula has been further alternating direction implicit iteration formula, used to take formula(that is, the ADI method) to solve differential equations, and gives the algorithm of the alternating direction implicit iteration method and program block diagram. Finally, with the tools of matlab programming solution. By solving the numerical example to illustrate the feasibility of this method, easy operation and wide application.