Meshless spectral method for solution of time-fractional coupled KdV equations

In this article, an efficient and accurate meshless spectral interpolation method is formulated for the numerical solution of time-fractional coupled KdV equations that govern shallow water waves. Meshless shape functions constructed via radial basis functions (RBFs) and point interpolation are used for discretization of the spatial operator. Approximation of fractional temporal derivative is obtained via finite differences of order O(τ2−α) and a quadrature formula. The formulated method is applied to various test problems available in the literature for its validation. Approximation quality and efficiency of the method is measured via discrete error norms E2, E∞ and Erms. Convergence analysis of the proposed method in space and time is numerically determined by varying nodal points M and time step-size τ respectively. Stability of the proposed method is discussed and affirmed computationally, which is an important ingredient of the current study.