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Journal of Scientific Research and Reports, ISSN: 2320-0227,Vol.: 3, Issue.: 21 (01-15 November)


Direct Solution of Initial Value Problems of Fourth Order Ordinary Differential Equations Using Modified Implicit Hybrid Block Method


S. J. Kayode1, M. K. Duromola1 and Bolarinwa Bolaji2*

1Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
2Department of Computer Sciences, Salem University, Lokoja, Nigeria.

Article Information


(1) Dr. Surapong Pinitglang, Department of Food Science and Technology, School of Science and Technology, University of the

Thai Chamber of Commerce, Thailand.

(2) Dr. Luigi Rodino, Professor of Mathematical Analysis, Dipartimento di Matematica, Università di Torino, Italy.


(1) Kaushik Bose, Vidyasagar University, India.

(2) Hala Hazam Al Otaibi, College of Agriculture and Food Science, King Faisal University, Saudi Arabia.

(3) Parvin Abedi, Ahvaz Jundishapur University of Medical Sciences, Iran.

(4) Anonymous, Nara Women’s University, Japan.

Complete Peer review History: http://www.sciencedomain.org/review-history/5926


Our focus in this article is the derivation; analysis and implementation of a new modified implicit hybrid block method for the direct solution of initial value problems of fourth order ordinary differential equations. In the derivation of the method, we adopted the approach of collocation approximation to obtain the main scheme with continuous coefficients. From the main scheme, additional schemes were developed. The implementation strategy of the new method is by combining the main scheme and the additional schemes as simultaneous integrator to initial value problem of fourth order ordinary differential equations. As required of any numerical method, the properties analysis of the block was done and the result showed that it is consistent, convergent, zero stable and absolutely stable. We then test our method with numerical examples solved using existing method and were found to give better results.

Keywords :

Interpolation; continuous coefficients; block method; numerical integration; fourth order ordinary differential equations.

Full Article - PDF    Page 2792-2800

DOI : 10.9734/JSRR/2014/11953

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