Higher Order Stable Numerical Algorithm for the Variable Order Time-Fractional Sub-diffusion Equation

In the present work, we proposed a numerical scheme for solving the Variable order time fractional sub-diffusion equation (VOTFSDE) by finite difference method. The variable order Caputo derivative is approximated by the L-123 approximation in time direction. The numerical schemes unconditional stability is theoretically investigated. The three test problems are used to execute the scheme, and the numerical results show a high level of accuracy and higher order of convergence. To show the efficiency and accuracy of our proposed scheme, a comparison of the numerical results with those from an earlier existing scheme is also provided.