SOLUTION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS,USING PREDICTOR - CORRECTOR METHODS

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Date
1987
Authors
AWOYEMI, DAVID ONI OLASEINDE
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Abstract
in this project, two classes of second order ordinary differential equations, y = f(x,y,y' ) with i n i t i a l conditions y(x 0 ) = y0 ,y (x 0) = y'0 and y = f(x,y) with y(x0)= yo, y' (X0) = y'0 were solved directly or as a system of two first order equations using the classical methods of Euler, Runge-Kutta, Adams-Moulton, Milne, Numerov and Taylor. Comparison of the methods and analysis of results were made. It was discovered that for the system ' y = f ( x , y , y ' ), Milne's method is better than Adams-Moulton's method in terms of numerical accuracies, execution times and memory allocations for all the step-sizes H considered, while Taylor series methods are found unsuitable for the t e s t problem and similar problems. For the system y' = f(x,y), however, Numerov's method is better than Milne's method, which in turn is still better than Adams-Moulton's method also in terms of numerical accuracies, execution times and memory allocations for all our H especially in problems where y K+1 can be made a subject in the Numerov's formula. Here, Taylor series method is found completely unsuitable for the test problem and similar problems.
Description
A thesis submitted to the Post—Graduate School, Ahmadu Bello university, Zaria in partial fulfilment of the requirements for the: degree of Master of Science (M.Sc.) in Mathematics.
Keywords
SOLUTION, SECOND, ORDER, ORDINAR, DIFFERENTIAL, EQUATIONS, ,USING, PREDICTOR, CORRECTOR, METHODS
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