Numerical solution of nonlinear SPDEs using a multi-scale method

Mohammadi Roozbahani, Mahmoud; Aminikhah, Hossein; Tahmasebi, Mahdieh

Numerical solution of nonlinear SPDEs using a multi-scale method

Document Type : Research Paper

Authors

¹ Faculty of Mathematical Sciences, University of Guilan, P. O. Box 19141-41938, Rasht, Iran

² Faculty of Mathematical Sciences, University of Guilan, P. O. Box 19141–41938, Rasht, Iran

³ Faculty of Mathematical Sciences, Tarbiat Modares University, P. O. Box 14115-134, Tehran, Iran

Abstract

‎In this paper we establish a new numerical method for solving a class of stochastic partial differential equations (SPDEs) based on B-splines wavelets‎. ‎The method combines implicit collocation with the multi-scale method‎. Using the multi-scale method‎, ‎SPDEs can be solved on a given subdomain with more accuracy and lower computational cost than the rest of the domain‎. ‎The stability and consistency of the method are provided‎. ‎Also numerical experiments illustrate the behavior of the proposed method‎.

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