A variational iteration method for solving Troesch’s problem

Troesch’s problem is an inherently unstable two-point boundary value problem. A new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve Troesch’s problem. The underlying idea of the method is to convert the hyperbolic-type nonlinearity i...

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Vydáno v:	Journal of computational and applied mathematics Ročník 234; číslo 10; s. 3043 - 3047
Hlavní autor:	Chang, Shih-Hsiang
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Kidlington Elsevier B.V 15.09.2010 Elsevier
Témata:	Algorithms Boundary value problems Calculus of variations and optimal control Exact sciences and technology Iterative methods Iterative solution Mathematical analysis Mathematical models Mathematics Nonlinearity Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Numerical methods in probability and statistics Sciences and techniques of general use Transformations Troesch’s problem Variable transformation Variational iteration method Troesch’s problem Variational iteration method Variable transformation Polynomial Troesch's problem Optimization method Iterative method Iteration Numerical method Stochastic method Algorithm Partial differential equation Numerical analysis Applied mathematics Two point boundary value problem Hyperbolic equation Analytical method Problem solving Variational calculus Nonlinearity Analytical solution Mathematical programming
ISSN:	0377-0427, 1879-1778
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Popis
Shrnutí:	Troesch’s problem is an inherently unstable two-point boundary value problem. A new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve Troesch’s problem. The underlying idea of the method is to convert the hyperbolic-type nonlinearity in the problem into polynomial-type nonlinearities by variable transformation, and the variational iteration method is then directly used to solve this transformed problem. Only the second-order iterative solution is required to provide a highly accurate analytical solution as compared with those obtained by other analytical and numerical methods.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2010.04.018