An efficient method for solving Troesch's problem

Shih Hsiang Chang, I-Ling Chang

研究成果: Article

3 引文 (Scopus)

摘要

Troesch's problem is an inherently unstable two-point boundary value problem. This paper describes an efficient method, in which the hyperbolic nonlinearity in Troesch's problem is first converted into the polynomial nonlinearity by variable transformation and the differential transform method is then used directly to solve this transformed problem. The approximate solution obtained is in the form of a rapid convergent power series and highly accurate in comparison with those obtained by other analytical and numerical methods. As compared with the differential transform method, this approach is more efficient and powerful since it provides a much faster convergent series solution with higher accuracy and considerably less computational effort. Finally, this method is successfully applied to other two-point boundary value problems with exponential nonlinearity and the obtained results demonstrate the reliability of the proposed approach.

原文English
頁(從 - 到)920-924
頁數5
期刊Advanced Science Letters
9
DOIs
出版狀態Published - 2012 七月 2

指紋

Boundary value problems
Differential Transform Method
Nonlinearity
nonlinearity
Two-point Boundary Value Problem
Variable Transformation
Numerical methods
transform
Series Solution
Polynomials
Analytical Methods
Power series
High Accuracy
Approximate Solution
Unstable
Numerical Methods
numerical method
analytical method
Polynomial
Reproducibility of Results

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Health(social science)
  • Mathematics(all)
  • Education
  • Environmental Science(all)
  • Engineering(all)
  • Energy(all)

引用此文

@article{1983fea5e91c4bea84db2a46424da481,
title = "An efficient method for solving Troesch's problem",
abstract = "Troesch's problem is an inherently unstable two-point boundary value problem. This paper describes an efficient method, in which the hyperbolic nonlinearity in Troesch's problem is first converted into the polynomial nonlinearity by variable transformation and the differential transform method is then used directly to solve this transformed problem. The approximate solution obtained is in the form of a rapid convergent power series and highly accurate in comparison with those obtained by other analytical and numerical methods. As compared with the differential transform method, this approach is more efficient and powerful since it provides a much faster convergent series solution with higher accuracy and considerably less computational effort. Finally, this method is successfully applied to other two-point boundary value problems with exponential nonlinearity and the obtained results demonstrate the reliability of the proposed approach.",
author = "Chang, {Shih Hsiang} and I-Ling Chang",
year = "2012",
month = "7",
day = "2",
doi = "10.1166/asl.2012.2611",
language = "English",
volume = "9",
pages = "920--924",
journal = "Advanced Science Letters",
issn = "1936-6612",
publisher = "American Scientific Publishers",

}

An efficient method for solving Troesch's problem. / Chang, Shih Hsiang; Chang, I-Ling.

於: Advanced Science Letters, 卷 9, 02.07.2012, p. 920-924.

研究成果: Article

TY - JOUR

T1 - An efficient method for solving Troesch's problem

AU - Chang, Shih Hsiang

AU - Chang, I-Ling

PY - 2012/7/2

Y1 - 2012/7/2

N2 - Troesch's problem is an inherently unstable two-point boundary value problem. This paper describes an efficient method, in which the hyperbolic nonlinearity in Troesch's problem is first converted into the polynomial nonlinearity by variable transformation and the differential transform method is then used directly to solve this transformed problem. The approximate solution obtained is in the form of a rapid convergent power series and highly accurate in comparison with those obtained by other analytical and numerical methods. As compared with the differential transform method, this approach is more efficient and powerful since it provides a much faster convergent series solution with higher accuracy and considerably less computational effort. Finally, this method is successfully applied to other two-point boundary value problems with exponential nonlinearity and the obtained results demonstrate the reliability of the proposed approach.

AB - Troesch's problem is an inherently unstable two-point boundary value problem. This paper describes an efficient method, in which the hyperbolic nonlinearity in Troesch's problem is first converted into the polynomial nonlinearity by variable transformation and the differential transform method is then used directly to solve this transformed problem. The approximate solution obtained is in the form of a rapid convergent power series and highly accurate in comparison with those obtained by other analytical and numerical methods. As compared with the differential transform method, this approach is more efficient and powerful since it provides a much faster convergent series solution with higher accuracy and considerably less computational effort. Finally, this method is successfully applied to other two-point boundary value problems with exponential nonlinearity and the obtained results demonstrate the reliability of the proposed approach.

UR - http://www.scopus.com/inward/record.url?scp=84862839925&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862839925&partnerID=8YFLogxK

U2 - 10.1166/asl.2012.2611

DO - 10.1166/asl.2012.2611

M3 - Article

AN - SCOPUS:84862839925

VL - 9

SP - 920

EP - 924

JO - Advanced Science Letters

JF - Advanced Science Letters

SN - 1936-6612

ER -