Numerical solution of stochastic elliptic partial differential equations using the meshless method of radial basis functions

Abstract

In this paper, we propose two numerical methods to solve the elliptic stochastic partial differential equations (SPDEs) in two and three dimensions obtained by Gaussian noises using radial basis functions (RBFs) collocation and pseudospectral (PS) collocation methods. For approximating the solution, generalized inverse multiquadrics (GIMQ) RBFs have been used. The Gaussian noises are approximated at the collocation points. The schemes work in a similar fashion as Hermite-based interpolation methods. The methods are tested via several problems. The numerical results show usefulness and accuracy of the new methods.