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

Volume 3, Issue 1, pp 21--34 Publication Date: July 20, 2011
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### 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.

### Keywords

• Compact finite difference
• Hyperbolic equations
• Krylov subspace methods
• Preconditioner.

•  65M06
•  35L72

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