TITLE:
An Accurate Five Off-Step Points Implicit Block Method for Direct Solution of Fourth Order Differential Equations
AUTHORS:
Monday Kolawole Duromola
KEYWORDS:
Interpolation, Continuous Coefficients, Block Method, Numerical Integration, Fourth Order Ordinary Differential Equations
JOURNAL NAME:
Open Access Library Journal,
Vol.3 No.6,
June
23,
2016
ABSTRACT:
In this article, my focus is the derivation, analysis and implementation
of a new modified one-step implicit hybrid block method with five off-step
points. The derived method is to solve directly initial value problems of
fourth order ordinary differential equations. The approach for the derivation of
the method is to interpolate the approximate power series solution to the
problem and to collocate its fourth derivative at the grid and off-grid points
to generate systems of linear equations for the determination of the unknown
parameters. The derived method is tested for consistency, zero stability,
convergence and absolute stability. Accuracy and usability of the method are
determined with some test problems and the results obtained are found to be
better in accuracy than some existing methods.