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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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