A GEOMETRICALLY CONVERGENT PSEUDO–SPECTRAL METHOD FOR MULTI–DIMENSIONAL TWO–SIDED SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Abstract

<abstract> In this study, we present a geometrically convergent numerical method for solving multi-dimensional two-sided space-time fractional differential equations. The approach represents the solutions of the differential equations in terms of the shifted Chebyshev polynomials. The expansions are evaluated at the shifted Chebyshev-Gauss-Lobatto nodes. We present the approximations for left-sided integration, and the left- and right- sided differentiation. The performance of the method is demonstrated using some two-sided space fractional partial differential equations in one and two dimensions. The numerical results obtained show that the method is accurate and computationally efficient. A theoretical analysis of the convergence of the method is presented, where it is shown that, given a continuously differentiable solution, the numerical solution converges for a sufficiently large number of grid points. </abstract>