## The homotopy analysis method to solve the Burgers-Huxley equation.(English)Zbl 1167.35483

Summary: An analytical technique, namely the homotopy analysis method (HAM) is applied to obtain an approximate analytical solution of the Burgers-Huxley equation. This paper introduces the two theorems which provide us with a simple and convenient way to apply the HAM to the nonlinear PDEs with the power-law nonlinearity. The homotopy analysis method contains the auxiliary parameter $$\hbar$$, which provides us with a simple way to adjust and control the convergence region of solution series.

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 35C10 Series solutions to PDEs 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 35G20 Nonlinear higher-order PDEs
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