International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2572

Full Length Research Paper

A four-point fully implicit method for the numerical integration of third-order ordinary differential equations

Awoyemi D. O
  • Awoyemi D. O
  • Department of Mathematics, Landmark University, Umuaru, Kwara State, Nigeria.
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Kayode S. J
  • Kayode S. J
  • Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
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Adoghe L. O.
  • Adoghe L. O.
  • Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State, Nigeria.
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  •  Accepted: 13 January 2013
  •  Published: 28 January 2014


In this paper, we derived a continuous linear multistep method (LMM) with step number k = 4 through collocation and interpolation techniques using power series as basis function for approximate solution. An order-seven scheme is developed which was used to solve the third-order initial value problems (IVPS) in ordinary differential equation without first reducing to a system first-order. Taylor’s series algorithm of the same order was developed to implement our method. The result obtained was compared favourably with existing methods.

Key words: Continuous collocation, multistep methods, interpolation, third-order, power series.