Solving Parabolic Equations Of High Accuracy Difference Scheme For Parallel Iterative Methods

Along with the development of science and technology, people study the depth and breadth of the problem is growing. In the natural sciences and technology in the field of modern engineering, the situation is a lot of use of parabolic equation or equations to describe . Therefore, the use of finite-difference approach to the numerical solution of parabolic equations with important questions of theoretical significance and application value. At solving parabolic equations of the problem, the necessary structure and high precision, good stability, storage capacity and computation of the difference scheme should be small. In this paper, the theory and practical application point of view, for the one-dimensional parabolic equation of the initial boundary value problem, using combinations of bad application of commercial law and parameters, structure and study the high-precision differential format and its parallel iterative algorithm, the text is divided into two major parts:First of all, the first part, a width of nodes in space 3, the time width of layer 3 node set of three partial structure on the design of a new differential equation with parameter, and give coefficient determined for a class of high-precision three-nine points with parameters implicit difference scheme to achieve the truncation error, and then using the Fourier method of stability analysis give a stability condition derived from the format, that is absolute and unconditional stability of the formatFollowed by the second part, in view of this article constructed implicit difference scheme, research was designed to solve parabolic differential equations of three-implicit iterative algorithm in parallel format, the basic idea is based on implicit difference equations of the characteristics of the coefficient matrix, the differential Equation group sub-divided into a number of equations to solve the iteration at the same time separately. In this paper, the structure of the process of this algorithm, and matrix theory proof of its convergence conditions and convergence of iterative direction. It has an absolute accuracy of order and stability, but also push the card at the time of mesh refinement convergence progressive in nature, that is, on the arbitrary grid and arbitrary than the sub-order equations, the iterative process of convergence and the convergence rate at each iteration With the points in the grid increases.Then give a specific example of the results of numerical experiments, a numerical example to verify the correctness of theoretical analysis, demonstrated the feasibility and effectiveness of algorithms.