Direct Algebraic Method for finding Complex Solutions of Huxley Equation

In this work, an efficient numerical method for the complex solutions of nonlinear partial differential equations based on the direct algebraic approach is proposed, and tested in the case of generalized Burgers–Huxley equation ∂u ∂t + αu ∂u ∂x − ∂ u ∂x2 = βu(1− u)(u − γ) Whenα = 0, δ = 1, is reduced to the Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction–diffusion equations. These calculations demonstrate that the accuracy of the direct algebraic solutions is quite high even in the case of a small number of grid points. The present method is a very reliable, simple, small computation costs, flexible, and convenient alternative method.