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Numerical solving for nonlinear using higher order homotopy Taylor-perturbation

Year 2013, Volume: 1 Issue: 1, 24 - 28, 01.04.2013

Nor Hanim Abd Rahman Arsmah Ibrahim Mohd İdris Jayes

Abstract

Rootfinding is a classical problem that still remains an interest to many researchers. A series of hybrid methods called Higher Order Homotopy Taylor-perturbation method via start-system functions (HTTPss) are implemented to give approximate solutions for nonlinear equations, . The techniques serve as alternative methods for obtaining approximate solutions for different types of nonlinear equations. Thus, this paper presents an analysis on numerical comparison between the classical Newton Raphson (CNR), Homotopy Perturbation method (HTPss) and Higher Order Homotopy Taylor-perturbation via start-system (HHTPss). A computational system Maple14 is used for this paper. Numerical and Illustrative results reveal that HHTPss methods are acceptably accurate and applicable

Keywords

HHTP NONLINEAR START SYSTEM

References

  • Chun,C., Bae, H.J. & Neta, B. 2009. New families of nonlinear third-order solvers for finding multiple roots. Computer and Mathematics with Applications 58:1574-1582.
  • He, J-H. 1999. Homotopy perturbation technique. Computer Methods in Applied Mechanic and Engineering 178:257-262.
  • He, J-H. 2009. An introduction to the homotopy perturbation method. Computer and Mathematics with applications. 57(3):410-412. Doi:1016/j.camwa.2008.06.003
  • Palancz, B., Awange, J.L & Lewis, R.H. 2010. Linear Homotopy Solution of Nonlinear Systems of Equations in Geodesy. J. Geod. Doi 1007/s100190-009-0346-x.
  • Pakdemirli, M. & Boyaci, H. 2007. Generation of root finding algorithms via perturbation theory and some formulas. Applied Mathematics and Computation, 184:783-788.
  • Rafig, A & Awais, M. 2008. Convergence on the Homotopy Continuation Method. International Journal of Applications Mathematics and Mechanics, 4(6):62-70.
  • Saeed, R.K. & Khthr, F.W. 2010. Three new iterative methods for solving nonlinear equations. Australian Journal of Basic & Applied Sciences 4(6):1022-1030.
  • S.G. Li, L.Z.Cheng & B.Neta. 2010. Some fourth-order nonlinear solvers with closed formulae for multiple roots. Computers and Mathematics with Applications 59:126-135

Numerical solving for nonlinear using higher order homotopy Taylor-perturbation

Year 2013, Volume: 1 Issue: 1, 24 - 28, 01.04.2013

Nor Hanim Abd Rahman Arsmah Ibrahim Mohd İdris Jayes

Abstract

References

  • Chun,C., Bae, H.J. & Neta, B. 2009. New families of nonlinear third-order solvers for finding multiple roots. Computer and Mathematics with Applications 58:1574-1582.
  • He, J-H. 1999. Homotopy perturbation technique. Computer Methods in Applied Mechanic and Engineering 178:257-262.
  • He, J-H. 2009. An introduction to the homotopy perturbation method. Computer and Mathematics with applications. 57(3):410-412. Doi:1016/j.camwa.2008.06.003
  • Palancz, B., Awange, J.L & Lewis, R.H. 2010. Linear Homotopy Solution of Nonlinear Systems of Equations in Geodesy. J. Geod. Doi 1007/s100190-009-0346-x.
  • Pakdemirli, M. & Boyaci, H. 2007. Generation of root finding algorithms via perturbation theory and some formulas. Applied Mathematics and Computation, 184:783-788.
  • Rafig, A & Awais, M. 2008. Convergence on the Homotopy Continuation Method. International Journal of Applications Mathematics and Mechanics, 4(6):62-70.
  • Saeed, R.K. & Khthr, F.W. 2010. Three new iterative methods for solving nonlinear equations. Australian Journal of Basic & Applied Sciences 4(6):1022-1030.
  • S.G. Li, L.Z.Cheng & B.Neta. 2010. Some fourth-order nonlinear solvers with closed formulae for multiple roots. Computers and Mathematics with Applications 59:126-135
There are 8 citations in total.

Details

Journal Section Articles
Authors

Nor Hanim Abd Rahman This is me

Arsmah Ibrahim This is me

Mohd İdris Jayes This is me

Publication Date April 1, 2013
Published in Issue Year 2013 Volume: 1 Issue: 1

Cite

APA Rahman, N. H. A., Ibrahim, A., & Jayes, M. İ. (2013). Numerical solving for nonlinear using higher order homotopy Taylor-perturbation. New Trends in Mathematical Sciences, 1(1), 24-28.
AMA Rahman NHA, Ibrahim A, Jayes Mİ. Numerical solving for nonlinear using higher order homotopy Taylor-perturbation. New Trends in Mathematical Sciences. April 2013;1(1):24-28.
Chicago Rahman, Nor Hanim Abd, Arsmah Ibrahim, and Mohd İdris Jayes. “Numerical Solving for Nonlinear Using Higher Order Homotopy Taylor-Perturbation”. New Trends in Mathematical Sciences 1, no. 1 (April 2013): 24-28.
EndNote Rahman NHA, Ibrahim A, Jayes Mİ (April 1, 2013) Numerical solving for nonlinear using higher order homotopy Taylor-perturbation. New Trends in Mathematical Sciences 1 1 24–28.
IEEE N. H. A. Rahman, A. Ibrahim, and M. İ. Jayes, “Numerical solving for nonlinear using higher order homotopy Taylor-perturbation”, New Trends in Mathematical Sciences, vol. 1, no. 1, pp. 24–28, 2013.
ISNAD Rahman, Nor Hanim Abd et al. “Numerical Solving for Nonlinear Using Higher Order Homotopy Taylor-Perturbation”. New Trends in Mathematical Sciences 1/1 (April 2013), 24-28.
JAMA Rahman NHA, Ibrahim A, Jayes Mİ. Numerical solving for nonlinear using higher order homotopy Taylor-perturbation. New Trends in Mathematical Sciences. 2013;1:24–28.
MLA Rahman, Nor Hanim Abd et al. “Numerical Solving for Nonlinear Using Higher Order Homotopy Taylor-Perturbation”. New Trends in Mathematical Sciences, vol. 1, no. 1, 2013, pp. 24-28.
Vancouver Rahman NHA, Ibrahim A, Jayes Mİ. Numerical solving for nonlinear using higher order homotopy Taylor-perturbation. New Trends in Mathematical Sciences. 2013;1(1):24-8.