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Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations

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  • Mohammad Alkasassbeh
  • Zurni Omar

Abstract

A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at while its second and third derivatives are collocated at all points in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.

Suggested Citation

  • Mohammad Alkasassbeh & Zurni Omar, 2017. "Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2017, pages 1-8, January.
    • Handle: RePEc:hin:jnljam:8510948
    DOI: 10.1155/2017/8510948
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    Cited by:

    1. D. Raymond & Y. Skwamw & J. Sunday, 2018. "An Implicit Two-Step One Off-Grid Point Third Derivative Hybrid Block Method for the Direct Solution of Second-Order Ordinary Differential Equations," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 4(2), pages 8-14, 02-2018.

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