Numerical solution of nonlinear SPDEs using a multi-scale method

‎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.