On Behavior of Preconditioned Methods for a Class of Compact Finite Difference Schemes in Solution of Hyperbolic Equations


Authors

A. Golbabai - Department of Applied Mathematics, Faculty of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran M. M. Arabshahi - Department of Applied Mathematics, Faculty of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran


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 compact finite difference schemes in solution of hyperbolic equations \(\alpha u_{tt}-\beta(X,t)u_{XX}=F(X,t,u,u_X,u_t)\) subject to appropriate initial and Dirichlet boundary conditions, where \(\alpha\) is constant. We show The BLAGE preconditioner is extremely effective in achieving optimal convergence rates. Numerical results performed on model problem to confirm the efficiency of our approach.


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