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