Five Steps Block Predictor-Block Corrector Method for the Solution of *y''* = *f* (*x*,*y*,*y'*)

Author(s)
Mathew Remilekun Odekunle,
Michael Otokpa Egwurube,
Adetola Olaide Adesanya,
Mfon Okon Udo

Affiliation(s)

Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria.

Department of Mathematics and Statistics, Cross River University of Technology, Calabar, Nigeria.

Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria.

Department of Mathematics and Statistics, Cross River University of Technology, Calabar, Nigeria.

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.

Keywords

Step Length, Power Series, Block Predictor, Block Corrector, Constant Order, Step Size, Grid Points, Self Starting, Efficiency

Step Length, Power Series, Block Predictor, Block Corrector, Constant Order, Step Size, Grid Points, Self Starting, Efficiency

Cite this paper

Odekunle, M. , Egwurube, M. , Adesanya, A. and Udo, M. (2014) Five Steps Block Predictor-Block Corrector Method for the Solution of*y''* = *f* (*x*,*y*,*y'*). *Applied Mathematics*, **5**, 1252-1266. doi: 10.4236/am.2014.58117.

Odekunle, M. , Egwurube, M. , Adesanya, A. and Udo, M. (2014) Five Steps Block Predictor-Block Corrector Method for the Solution of

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