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An efficient analytic approach for solving two‐point nonlinear boundary value problems by homotopy analysis method
Author(s) -
Hassan Hany N.,
ElTawil Magdy A.
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1416
Subject(s) - homotopy analysis method , mathematics , nonlinear system , convergence (economics) , boundary value problem , homotopy , scheme (mathematics) , convergent series , differential equation , mathematical optimization , mathematical analysis , pure mathematics , physics , quantum mechanics , economics , economic growth , power series
In this paper, we use 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 importance of choice of convergence‐control parameter ℏ to guarantee the convergence of the solutions of nonlinear differential equations. 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. Copyright © 2011 John Wiley & Sons, Ltd.