Matrix technology for a class of fourth-order difference schemes in solution of hyperbolic equations

Abstract

In this article, We apply Krylov subspace methods in combination of the ADI, BLAGE,... method as a preconditioner for a class of linear systems arising from fourth-order finite difference schemes in = solution of hyperbolic equations subject to appropriate initial and Dirichlet boundary conditions, where \u03b1 is constant. We show The BLAGE preconditioner is extremely effective in achieving optimal convergence rates for the class of fourth-order difference schemes considered in this paper. Numerical results performed on model problem to confirm the efficiency of our approach.