A CLASS OF BLOCK MULTISTEP METHODS FOR SOLVING GENERAL THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Oghonyon, J. G. (2016) A CLASS OF BLOCK MULTISTEP METHODS FOR SOLVING GENERAL THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS. ["eprint_fieldopt_thesis_type_phd" not defined] thesis, Covenant University, Nigeria..

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Abstract

The numerical solutions of general third order initial value problems of ordinary di�erential equations have been studied in this research work. A new class of block multistep methods capable of solving general third order IVPs of ODEs using variable step size technique have been developed. Collocation and interpolation of power series as the approximate solution is adopted. The block multistep method was intensi�ed by the introduction of continuous scheme in order to circumvent the limitation created by reducing to systems of �rst order ODEs. The new class of variable step-size method has the advantage to control and minimize error, determine and vary the step size as well as decide the prescribed tolerance level to ascertain the maximum errors. Some theoretical properties of the block multistep methods such as order of the scheme, zero stability, consistency and determination of the region of absolute stability of the scheme have been conducted and presented. Numerical examples on nonsti� IVPs have been used to test the performance of the methods, in addition, comparing the maximum error as the prescribed tolerance parameter level is reduced in the method. The newly developed methods have been written as mathematical program and expressed in form of mathematical language which can run simultaneously when implemented. The newly formulated variable step-size block multistep methods perform better when compared with other existing methods as the prescribed tolerance parameter level got smaller and smaller. Furthermore, the newly developed methods possess the attribute to control and decide on the estimate of the actual step size that will guarantee an improved results with better maximum errors. This, in particular, is seen as an advantage of the variable step size method over other existing methods approximated with �xed step size. Finally, the idea of predictor-corrector methods used by various researchers to predict and correct estimates has been extended in the newly proposed method to change/decide on suitable step size, determine the prescribed tolerance level and error control/minimization.

Item Type:	Thesis (["eprint_fieldopt_thesis_type_phd" not defined])
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Mrs Hannah Akinwumi
Date Deposited:	08 Jul 2016 12:50
Last Modified:	02 Dec 2016 11:18
URI:	http://eprints.covenantuniversity.edu.ng/id/eprint/6738

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