Application of meshfree spectral method for the solution of multi-dimensional time-fractional Sobolev equations

Abstract The present study aims to formulate a meshfree spectral method to numerically solve multi-dimensional time-fractional Sobolev equations. In this method radial basis functions and point interpolation approach is utilized to build meshfree shape functions. These shape functions, having Kronecker delta function property, are then used for spatial discretization. Forward difference formula, in alignment to a quadrature rule, is used for temporal disctrezation. Validation of the proposed method is made by considering various test examples from literature. Simulated results reveal very good agreement with available exact solutions which are reported in graphical and tabulated forms. Approximation quality and efficiency of the current method is achieved in terms of e2, e∞ and erms error norms, number of collocation points as well as time-step size. Stability of the proposed method is thoroughly analyzed and discussed.

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