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An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method
Mathematical Methods in the Applied Sciences • 2011
Publication Information
Authors
Hany N. Hassan; Magdy A. El-Tawil
Keywords
homotopy analysis method; two point nonlinear boundary value problems; convergence-controller parameter; Taylor
expansion; Troesch’s problem; Bratu’s equation
Journal
Mathematical Methods in the Applied Sciences
Publisher
John Wiley & Sons, Ltd
Volume
34
Issue
Not Available
Pages
977–989
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
n 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 h 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.
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 h 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.