An efficient algorithm for solving Troesch's problem

Applied Mathematics and Computation

Volumn 189, Issue 1, 2007, Pages 500-507

  Feng, Xinlong ^a,b   Mei, Liquan ^b   He, Guoliang ^b  

^a XINJIANG UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Adomian decomposition method; Homotopy perturbation technique; Taylor expansion; Troesch's problem; Variational iteration method

Indexed keywords

COMPUTATIONAL METHODS; ITERATIVE METHODS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

ADOMIAN DECOMPOSITION METHOD; HOMOTOPY PERTURBATION TECHNIQUE; TAYLOR EXPANSION; TROESCH'S PROBLEM; VARIATIONAL ITERATION METHOD;

ALGORITHMS;

EID: 34248395626     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.11.161     Document Type: Article

References (24)

1. Abramowitz M., and Stegun I. Handbook of Mathematical Functions (1972), Dover, New York
2. Erdélyi A., Magnus W., Oberhettinger F., and Tricomi F.G. Higher Transcendental Functions vol. 2 (1953), McGraw-Hill, New York
3. Roberts S.M., and Shipman J.S. On the closed form solution of Troesch's problem. J. Comput. Phys. 21 (1976) 291
4. Weibel E.S. In: Landshoff R.K.M. (Ed). The Plasma in Magnetic Field (1958), Stanford University Press, Stanford
5. Troesch B.A. A simple approach to a sensitive two-point boundary value problem. J. Comput. Phys. 21 (1976) 279
6. Deeba E., Khuri S.A., and Xie S. An algorithm for solving boundary value problems. J. Comput. Phys. 159 (2000) 125-138
7. Shaher Momani, Salah Abuasad, Zaid Odibat, Variational iteration method for solving nonlinear boundary value problems, Appl. Math. Comput., Available online 2 August 2006.
8. Scott M.R., and Watts H.A. A systemized collection of codes for solving two-point boundary-value problems. Numerical Methods for Differential Systems (1976), Academic Press
9. M.R. Scott, H.A. Watts, Computational solution of nonlinear two-point boundary-value problems, in: Proceedings of the Fifth Symposium Computers in Chemical Engineering, 1977, pp. 17-28.
10. Scott M.R., and Watts H.A. Computational solution of linear two-point boundary value problems via orthonormalization. SIAM J. Numer. Anal. 14 1 (1977) 40-70
11. Watson L.M., and Scott M.R. Solving spline-collocation approximations to nonlinear two-point boundary-value problems by a homotopy method. Appl. Math. Comput. 24 4 (1987) 333-357
12. Liao S.J. A challenging nonlinear problem for numerical techniques. J. Comput. Appl. Math. 181 (2005) 467-472
13. Liao S.J. Beyond Perturbation: Introduction to the Homotopy Analysis Method (2003), Chapman & Hall/CRC, Boca Raton
14. Liao S.J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl. Math. Comput. 169 2 (2005) 1186-1194
15. He J.H. Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput. 135 1 (2003) 73
16. He J.H. Comparison of homotopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156 2 (2004) 527
17. He J.-H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simul. 6 2 (2005) 207
18. He J.-H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20 10 (2006) 1141-1199
19. Abd El-Latif G.M. A homotopy technique and a perturbation technique for non-linear problems. Appl. Math. Comput. 169 (2005) 576-588
20. Nayfeh A.H. Perturbation Methods (2000), Wiley, New York
21. Holmes M.H. Introduction to Perturbation Methods (1995), Springer, Berlin
22. Wazwaz A.M. Adomian decomposition method for a reliable treatment of the Bratu-type equations. Appl. Math. Comput. 166 (2005) 152-633
23. Xinlong Feng, Yinnian He, High order iterative methods without derivatives for solving nonlinear equations, Appl. Math. Comput., Available online 2 October 2006.
24. Casha J.R., and Mazzia F. A new mesh selection algorithm, based on conditioning, for two-point boundary value codes. J. Comput. Appl. Math. 184 2 (2005) 362-381