On Behavior of Preconditioned Methods for a Class of Compact Finite Difference Schemes in Solution of Hyperbolic Equations
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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.
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ISRP Style
A. Golbabai, M. M. Arabshahi, On Behavior of Preconditioned Methods for a Class of Compact Finite Difference Schemes in Solution of Hyperbolic Equations, Journal of Mathematics and Computer Science, 3 (2011), no. 1, 21--34
AMA Style
Golbabai A., Arabshahi M. M., On Behavior of Preconditioned Methods for a Class of Compact Finite Difference Schemes in Solution of Hyperbolic Equations. J Math Comput SCI-JM. (2011); 3(1):21--34
Chicago/Turabian Style
Golbabai, A., Arabshahi, M. M.. "On Behavior of Preconditioned Methods for a Class of Compact Finite Difference Schemes in Solution of Hyperbolic Equations." Journal of Mathematics and Computer Science, 3, no. 1 (2011): 21--34
Keywords
- Compact finite difference
- Hyperbolic equations
- Krylov subspace methods
- Preconditioner.
MSC
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