The role of coefficients of a general SPDE on the stability and convergence of a finite difference method |
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Authors: | Minoo Kamrani |
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Institution: | Department of Mathematics, Faculty of sciences, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran |
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Abstract: | In this paper for the approximate solution of stochastic partial differential equations (SPDEs) of Itô-type, the stability and application of a class of finite difference method with regard to the coefficients in the equations is analyzed. The finite difference methods discussed here will be either explicit or implicit and a comparison between them will be reported. We prove the consistency and stability of these methods and investigate the influence of the multiplier (particularly multiplier of the random noise) in mean square stability. From stochastic version of Lax-Richtmyer the convergence of these methods under some conditions are established. Numerical experiments are included to show the efficiency of the methods. |
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Keywords: | 60H15 65M06 65M12 |
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