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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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 234; no. 10; pp. 3043 - 3047
Main Author: Chang, Shih-Hsiang
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 15.09.2010
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography: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