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Zbl 1226.34021
Hassan, Hany N.; El-Tawil, Magdy A.
An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method. (English)
[J] Math. Methods Appl. Sci. 34, No. 8, 977-989 (2011). ISSN 0170-4214; ISSN 1099-1476/e

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.
[Feng Xie (Shanghai)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34A45 Theoretical approximation of solutions of ODE
34A25 Analytical theory of ODE

Keywords: homotopy analysis method; two point nonlinear boundary value problems; convergence-controller parameter; Taylor expansion; Troesch's problem; Bratu's equation

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Zentralblatt MATH Berlin [Germany]