A kernel‐based pseudo‐spectral method for multi‐term and distributed order time‐fractional diffusion equations

Abstract

In this paper, we focus on the study of a kernel-based method in pseudo-spectral (PS) mode for multi-term and distributed order time-fractional diffusion equations. Using the theory of reproducing kernel, reproducing kernel functions will be established in reproducing kernel Hilbert space. In the proposed method, a finite difference scheme is used in temporal space to achieve a semi-discrete configuration. Then, with the help of the kernel-based PS method, we will illustrate how to derive the numerical solution. Finally, to support the accuracy and efficiency of the proposed method, we provide several numerical examples. In numerical experiments, the quality of the approximation is calculated by absolute error and discrete error norms.

Spectral Element Method for Fractional Klein–Gordon Equations Using Interpolating Scaling Functions

“…So, numerical approaches can address this deficiency. Here, we mention some of these methods, including finite difference method [17], collocation method [18,19], Galerkin method [20,21], finite element method [22], kernelbased pseudo-spectral method [23], nonuniform difference schemes [24], and fractional differential transform method [25].…”