A Linearized Method for Multi‐Term Time‐Fractional Nonlinear Diffusion Equations With Initial Singularity

ABSTRACT In this paper, we construct a linearized finite difference scheme for a class of multi‐term time‐fractional nonlinear diffusion equations (MTFNDEs) with initial boundary value conditions. Due to the initial singularity of the solutions of MTFNDEs, it is well known that many existing numerical methods for MTFNDEs often suffer from the phenomenon of order reduction. In order to solve the above problem, based on the technique of variable transformation , we propose an improved Euler method to solve MTFNDEs. Then, we prove that the scheme has order accuracy in time for . Meanwhile, the unconditional stability and convergence of the scheme are proved through the energy method. Finally, numerical experiments have been conducted to support the theoretical results and efficiency of our proposed scheme.