An efficient class of discrete finite difference/element scheme for solving the fractional reaction subdiffusion equation

Abstract

An estimate for the fractional reaction subdiffusion equation is presented by a discrete Crank-Nicolson finite element method (FEM), which we can obtain by using the finite difference method (FDM) (in time) and the finite element method (in space). The proposed scheme is obtained at time t n+ 1 2 because at this time there are some different coefficients compared to those at time t n+1 , that is,. We studied the stability analysis, truncation error, and convergence analysis of the derived scheme. Numerical examples are presented to illustrate the efficiency of the given algorithm.

An Accurate Approach to Simulate the Fractional Delay Differential Equations

“…Since explicit exact solutions for FDEs are still lacking, approximation and numerical techniques such as the spectral collocation method (SCM), FEM, FVM, and many others have been used to solve many fractional models [11][12][13][14][15]. The paper's primary goal is to use the mentioned algorithm ( [16,17]) to obtain the numerical solution of the following FDDE using SCM depending on the fractional Legendre polynomials [18]:…”