Meshless RBFs method for numerical solutions of two-dimensional high order fractional Sobolev equations

Abstract

In this paper, meshless RBFs method is proposed to solve two-dimensional time-fractional Sobolev equations. The proposed method uses RBFs for approximation of spatial operator. Finite difference formula of O(δt2−α)(0<α≤1) is used for time-fractional derivative approximation while θ-rule (0≤θ≤1) as time stepping scheme for the advancement of solution in time. Validation of the proposed method is made by considering various test examples from literature. Simulated results are found in very good agreement with available exact solutions. A rigorous comparative analysis made with other methods testifies proposed method’s superiority in higher dimensions. Efficiency and accuracy of RBFs method are examined by varying number of nodes N in the domain of influence, time-step size δt, as well as L2, L∞ and Lrms error norms. Linearized stability analysis of the proposed method is thoroughly discussed and verified numerically to support the analysis.