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Approximate analytical solutions of systems of PDEs by homotopy analysis method. (English) Zbl 1142.65423
Summary: In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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