Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration

J. Sulaiman, Mohammad Khatim Hasan, M. Othman, S. A. Abdul Karim

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

Abstract

In previous studies, the effectiveness of the second-order quarter-sweep finite difference approximation equations has been shown in solving singularly perturbed boundary value problems. In this paper, however, we investigate the application of the fourth-order quarter-sweep finite difference approximation equation based on the fourth-order standard central difference scheme. To solve the problems numerically, discretization of the singularly perturbed problems via second-order and fourth-order finite difference schemes is proposed to form the corresponding system of linear algebraic equations. For comparison purpose, we also discuss on how to derive the basic formulation and implementation for the family of Successive Over-Relaxation (SOR) iterative methods such as FSSOR, HSSOR and QSSOR in solving the corresponding linear systems generated from the fourth-order discretization schemes based on full, half- and quarter-sweep cases. Some numerical tests were conducted to show that the accuracy of fourth-order finite difference schemes via the corresponding GS methods is more accurate than second-order schemes.

Original languageEnglish
Title of host publicationAIP Conference Proceedings
Pages275-284
Number of pages10
Volume1522
DOIs
Publication statusPublished - 2013
Event20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012 - Putrajaya
Duration: 18 Dec 201220 Dec 2012

Other

Other20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012
CityPutrajaya
Period18/12/1220/12/12

Fingerprint

boundary value problems
iteration
linear equations
linear systems
approximation
formulations

Keywords

  • Quarter-sweep reduction technique
  • SOR iteration
  • Standard finite difference scheme

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Sulaiman, J., Hasan, M. K., Othman, M., & Abdul Karim, S. A. (2013). Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration. In AIP Conference Proceedings (Vol. 1522, pp. 275-284) https://doi.org/10.1063/1.4801134

Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration. / Sulaiman, J.; Hasan, Mohammad Khatim; Othman, M.; Abdul Karim, S. A.

AIP Conference Proceedings. Vol. 1522 2013. p. 275-284.

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

Sulaiman, J, Hasan, MK, Othman, M & Abdul Karim, SA 2013, Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration. in AIP Conference Proceedings. vol. 1522, pp. 275-284, 20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012, Putrajaya, 18/12/12. https://doi.org/10.1063/1.4801134
Sulaiman J, Hasan MK, Othman M, Abdul Karim SA. Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration. In AIP Conference Proceedings. Vol. 1522. 2013. p. 275-284 https://doi.org/10.1063/1.4801134
Sulaiman, J. ; Hasan, Mohammad Khatim ; Othman, M. ; Abdul Karim, S. A. / Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration. AIP Conference Proceedings. Vol. 1522 2013. pp. 275-284
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