On a new weight tri-diagonal iterative method and its applications

In this article, a new weight tri-diagonal iterative method in solving system of linear equation is proposed and its convergence is discussed. The set of methods in solving linear system generated by high-order scheme for solving one-dimensional Poisson equation and one-dimensional heat equation with periodic boundary are presented. The numerical experiments shows that the proposed method demonstrates a better performance compared with weight Jacobi, successive-over relaxation and alternating group explicit methods.