An implicit graded mesh-based numerical scheme for multi-term time fractional nonlinear Fisher’s equation

Abstract This article presents an implicit difference scheme utilizing a temporally graded mesh to solve the multi-term time-fractional generalized Fishers’ equation using the Caputo derivative. The non-smooth solution of this problem exhibits a weak singularity in the vicinity of t = 0, which cannot be effectively managed using uniform meshes. Therefore, we present an unconditionally stable and convergent scheme based on the non-uniform mesh using the grading parameter. The quasilinearization technique is used to linearize the nonlinear term. The numerical outcomes demonstrate that employing a non-uniform graded mesh yields more effective and accurate results than a uniform mesh when dealing with non-smooth solutions.