The Study On Alternating Direction Algorithm For Numerical Solution Of A Class Of Partial Differential Equations

Partial differential equation has been widely used in the natural sciences and engineering technology,and many of the mathematical models can be described with the partial differential equation.Besides,many important basic equations of physics,mechanics or some other disciplines are themselves partial differential equation.In recent decades,the development of partial differential equation is very fast,and the research achievements are endless.Exploring the numerical solution method of partial differential equation has always been a hotspot.The alternating direction implicit(ADI)method is a kind of solution algorithm with simple discrete process,fast computation speed,high calculation accuracy,and easy programming.In this paper,the alternating direction implicit method for the numerical solution of a class of partial differential equations with variable coefficients is systematically studied,which mainly includes the following aspects.1.The related background and the significance of the partial differential equation are expounded,and the new progress of the research at home and abroad is summarized.The research work of this paper is arranged in detail,and the related preliminary knowledge is given.2.The iterative format solved by the alternating direction implicit(ADI)method is given for a class of partial differential equations with variable coefficients(including two dimensional parabolic equation,two and three dimensional elliptic equations).The corresponding truncation error analysis theory is established,and the numerical simulation and the results analysis are given,then the iterative parameters in the iteration process are discussed.3.The algorithm design is carried out respectively for the alternating direction implicit format of a class of partial differential equations with variable coefficients proposed,and the general solution program is compiled.