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An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method. (English) Zbl 1226.34021
Authors’ abstract: We use the homotopy analysis method (HAM) to solve two-point nonlinear boundary value problems that have at least one solution. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The scheme shows the importance of the choice of the convergence-control parameter $\hbar$. This scheme is tested on three nonlinear exactly solvable differential equations. Two of the examples are practical in science and engineering. The results demonstrate reliability, simplicity and efficiency of the algorithm developed.

##### MSC:
 34B15 Nonlinear boundary value problems for ODE 34A45 Theoretical approximation of solutions of ODE 34A25 Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
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