Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration

Jumat Sulaiman, Mohammad Khatim Hasan, Mohamed Othman, Samsul Ariffin Abdul Karim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

In this paper, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method together with Newton scheme namely Newton-HSSOR is investigated in solving the nonlinear systems generated from the fourth-order half-sweep finite difference approximation equation for nonlinear two-point boundary value problems. The Newton scheme is proposed to linearize the nonlinear system into the form of linear system. On top of that, we also present the basic formulation and implementation of Newton-HSSOR iterative method. For comparison purpose, combinations between the Full-Sweep Gauss-Seidel (FSGS) and Full-Sweep Successive Over-Relaxation (FSSOR) iterative methods with Newton scheme, which are indicated as Newton-FSGS and Newton-FSSOR methods respectively have been implemented numerically. Numerical experiments of two problems are given to illustrate that the Newton-HSSOR method is more superior compared with the tested methods.

Original languageEnglish
Title of host publicationAIP Conference Proceedings
PublisherAmerican Institute of Physics Inc.
Pages69-75
Number of pages7
Volume1602
ISBN (Print)9780735412361
DOIs
Publication statusPublished - 2014
Event3rd International Conference on Mathematical Sciences, ICMS 2013 - Kuala Lumpur
Duration: 17 Dec 201319 Dec 2013

Other

Other3rd International Conference on Mathematical Sciences, ICMS 2013
CityKuala Lumpur
Period17/12/1319/12/13

Fingerprint

boundary value problems
newton
iteration
nonlinear systems
linear systems
formulations
approximation

Keywords

  • Fourth-order scheme
  • Nonlinear two-point boundary value problem
  • SOR iteration

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Sulaiman, J., Hasan, M. K., Othman, M., & Karim, S. A. A. (2014). Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration. In AIP Conference Proceedings (Vol. 1602, pp. 69-75). American Institute of Physics Inc.. https://doi.org/10.1063/1.4882468

Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration. / Sulaiman, Jumat; Hasan, Mohammad Khatim; Othman, Mohamed; Karim, Samsul Ariffin Abdul.

AIP Conference Proceedings. Vol. 1602 American Institute of Physics Inc., 2014. p. 69-75.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sulaiman, J, Hasan, MK, Othman, M & Karim, SAA 2014, Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration. in AIP Conference Proceedings. vol. 1602, American Institute of Physics Inc., pp. 69-75, 3rd International Conference on Mathematical Sciences, ICMS 2013, Kuala Lumpur, 17/12/13. https://doi.org/10.1063/1.4882468
Sulaiman J, Hasan MK, Othman M, Karim SAA. Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration. In AIP Conference Proceedings. Vol. 1602. American Institute of Physics Inc. 2014. p. 69-75 https://doi.org/10.1063/1.4882468
Sulaiman, Jumat ; Hasan, Mohammad Khatim ; Othman, Mohamed ; Karim, Samsul Ariffin Abdul. / Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration. AIP Conference Proceedings. Vol. 1602 American Institute of Physics Inc., 2014. pp. 69-75
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