Quasi Multigrid Preconditioned Iteration Method And Numerical Experiment

Partial differential equations have an important role in modern mathematics, mostpartial differential equations can not be solved analytically, but rather use the numericalsolution to approximate the numerical solution of partial differential equations there aremany ways one of the more important one is multi-grid method, the multi-grid methodaccording speed than the traditional iterative methods improved, but also for the thecondition relatively large number of ill-conditioned matrix slightly less than, thepre-processing method can solve the coefficient matrix condition number overthe bigproblem, to be the multigrid preconditioned iteration method is a combination of theaforementioned advantages of both methods proposed. Due to the proposed multi-gridpre-iteration method to solve the one-dimensional elliptic equations boundary valueproblem has achieved good results, this paper will be extended to the initial boundaryvalue problem of the one-dimensional parabolic equation. The thesis is divided into thefollowing two parts:1, the multi-grid method and pretreatment iterative method effective combinationof initial boundary value problem for solving one-dimensional parabolic partialdifferential equations. Solving the boundary value problem of one-dimensional ellipticequations proposed multigrid preconditioned iteration method is extended to theone-dimensional parabolic equation, initial boundary value problem to construct theproposed multi-grid preconditioned iteration format.2, according to the calculation procedure of the above algorithm, write a fortranprogram for solving one-dimensional parabolic partial differential equation with initialboundary value problem through specific mathematical model, the numerical test resultswere compared with the calculated results with the SOR method.Numerical experiments show that the new method on the convergence rate is muchbetter than the SOR method, the new method on the dependence of the relaxation factoris not strong, the convergence rate is not volatility because small changes in relaxationfactor, which is the new the strengths of the method.