An analytic algorithm for time fractional nonlinear reaction–diffusion equation based on a new iterative method

A new analytic algorithm for highly nonlinear time fractional reaction–diffusion equations is proposed in this paper. The proposed method is an amalgamation of variational iteration method (VIM), Adomian decomposition method (ADM) and further refined by introducing a new correction functional. This new correction functional is obtained from the standard correction functional of VIM by introducing an auxiliary parameter γ and an auxiliary function H(x) in it. Further, a sequence Gn(x, t), with suitably chosen support, is also introduced in the new correction functional. The algorithm is easy to implement and only four to six iterations are sufficient for fairly accurate solutions. The algorithm is tested on Fitzhugh – Nagumo and generalized Fisher equations with nonlinearity ranging from 2 to 5.

► A new iterative method is developed to propose a hybrid algorithm for the highly nonlinear reaction–diffusion equations.
► The method is an amalgamation of VIM, ADM and further refined by introducing a new correction functional.
► We decompose the source term g(x, t) as a finite sum and construct a sequence Gn(x, t) → g(x, t) and use it in the new correction functional as well.