TITLE:
Five Steps Block Predictor-Block Corrector Method for the Solution of y'' = f (x,y,y')
AUTHORS:
Mathew Remilekun Odekunle, Michael Otokpa Egwurube, Adetola Olaide Adesanya, Mfon Okon Udo
KEYWORDS:
Step Length, Power Series, Block Predictor, Block Corrector, Constant Order, Step Size, Grid Points, Self Starting, Efficiency
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.8,
May
8,
2014
ABSTRACT: Theory has it that
increasing the step length improves the accuracy of a method. In order to
affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power
series approximate solution at some selected grid points is considered so as to
generate continuous linear multistep methods with constant step sizes. Two,
three and four interpolation points are considered to generate the continuous
predictor-corrector methods which are implemented in block method respectively.
The proposed methods when tested on some numerical examples performed more
efficiently than those of [1]. Interestingly the concept of self starting [2] and that of
constant order are reaffirmed in our new methods.