Alternating-triangular iterative method for the solution of difference elliptic equations in a rectangle. (English. Russian original) Zbl 0598.65078

Kucherov, A. B.; Nikolaev, E. S.

U.S.S.R. Comput. Math. Math. Phys. 16(1976), No. 5, 74-85 (1977); translation from Zh. Vychisl. Mat. Mat. Fiz. 16, 1164-1174 (1976).

We study an alternating-triangle iteration method of A. A. Samarskij for the solution of the Dirichlet difference problem for a second order elliptic equation with variable coefficients in a rectangle. In Section One we describe a generalized variant of the method and estimate the number of iterations. In Section Two we construct a variant of the iteration method for the proposed difference problem. We prove the convergence of the method with the number of iterations \(O(h^{-1/2}\ln \epsilon^{-1})\), where h is the mesh step and \(\epsilon\) is the accuracy. In Section Three we present an algorithm for the method and the results of numerical experiments.

MSC:

65N22	Numerical solution of discretized equations for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
35J25	Boundary value problems for second-order elliptic equations

Keywords:

alternating-triangle iteration method; variable coefficients; convergence; numerical experiments