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 |
| 卷 | 9 |
| DOIs | |
| 出版狀態 | Published - 2012 七月 2 |
指紋
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
}
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 -