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A Four-step Collocation Procedure by means of Perturbation term with Application to Third-order Ordinary Differential Equation
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 175 - Number 24 |
| Year of Publication: 2020 |
| Authors: Aigbiremhon Augustine Aizenofe, Omole Ezekiel Olaoluwa |
10.5120/ijca2020920774
|
Aigbiremhon Augustine Aizenofe, Omole Ezekiel Olaoluwa . A Four-step Collocation Procedure by means of Perturbation term with Application to Third-order Ordinary Differential Equation. International Journal of Computer Applications. 175, 24 ( Oct 2020), 25-36. DOI=10.5120/ijca2020920774
Abstract
In this paper, we developed a new method within an interval of four for numerical solution of third-order ordinary differential equations. Interpolation and collocation approach was used by choosing interpolation points at steps points using power series, while collocation points at step points. The method adopts a combination of powers series and perturbation terms gotten from the Legendre polynomials, giving rise to a polynomial of degree and equations. All the analysis on the derived method shows that it is stable has order of accuracy p=2, convergent and the region is absolutely stable. Numerical examples were provided to test the performance of the new method. The developed method was used to solve problems ranging from linear, non-linear and non-stiff Problem to test the applicability of the new method. Results obtained when compared with existing methods in the literature shows that the method is accurate, efficient and computational reliable.
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