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Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 1 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 2 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 3 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 4 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
American Journal of Computational Mathematics·Volume 04 (2014)·Pages 280–288·Published 29 August 2014·DOI10.4236/ajcm.2014.44024
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Abstract
Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and mathematical sciences. In this paper we use three finite difference schemes in order to approximate the solution of stochastic parabolic partial differential equations. The conditions of the mean square convergence of the numerical solution are studied. Some case studies are discussed.
KeywordsStochastic Partial Differential EquationsMean Square SenseSecond Order Random VariableFinite Difference Scheme
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