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Implicit two-point block method with third and fourth derivatives for solving general second order ODEs


Citation

Allogmany, Reem Ayed and Ismail, Fudziah and Ibrahim, Zarina Bibi (2019) Implicit two-point block method with third and fourth derivatives for solving general second order ODEs. Mathematics and Statistics, 7 (4). pp. 116-123. ISSN 2332-2071; ESSN: 2332-2144

Abstract

In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates the first and second derivatives of f(x; y; y 0), which are the third and fourth derivatives of the solution. The method is derived using Hermite Interpolating Polynomial as the basic function. A performance comparison of the two-point block method is compared in term of accuracy to several existing methods, which have order almost equal or higher than that of the new method. Numerical results interpret the accuracy and efficacy of the new method. Application of the new method is discussed.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.13189/ms.2019.070404
Publisher: Horizon Research Publishing
Keywords: Implicit; Block method; Second order ODEs; Hermite interpolation
Depositing User: Azhar Abdul Rahman
Date Deposited: 01 Oct 2020 03:29
Last Modified: 01 Oct 2020 03:29
Altmetrics: http://altmetrics.com-details.php?domain=psair.upm.edu.my&doi= 10.13189/ms.2019.070404
URI: http://psasir.upm.edu.my/id/eprint/80180
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