A Class of Implicit Five Step Hybrid Method for Solving First Order Initial Value Problem
1 Department of Mathematical Sciences, Federal University Gusau, P. M. B. 1001, Gusau, Zamfara State, Nigeria.
2 Department of Mathematics/Statistics, Federal University of Technology, P. M. B. 65, Minna, Niger State, Nigeria.
* Corresponding author: laminukaura@gmail.com
2 Department of Mathematics/Statistics, Federal University of Technology, P. M. B. 65, Minna, Niger State, Nigeria.
* Corresponding author: laminukaura@gmail.com
Abstract
In this paper, a self-starting five step continuous block hybridformulae (CBHF) with one Off-step point is developed using col-location and interpolation procedures. The CBHF is then used toproduce multiple numerical integrators that are of uniform orderand are assembled in to a single block matrix equation. Theseequations are simultaneously applied to provide the approximatesolution for the ordinary differential equations. The order ofaccuracy of the block method was discussed and its accuracy overthe methods in literature is established numerically. The resultof the proposed hybrid method performed absolutely better,when compared with the exact solution and the result obtainedby Mohammed (2011), which are all of step five (i.e. k = 5).
Keywords
Collocation and Interpolation
Continuous Hybrid Block Formulae
Off-Step Points
Stability
Stiff ODEs
How to Cite
Idris, L., Yahaya, Y. A., & Mohammed, U. (2018). A Class of Implicit Five Step Hybrid Method for Solving First Order Initial Value Problem. Nigerian Journal of Mathematics and Applications, 27(1), 99-107.
L. Idris, Y. A. Yahaya, and U. Mohammed, "A Class of Implicit Five Step Hybrid Method for Solving First Order Initial Value Problem," Nigerian Journal of Mathematics and Applications, vol. 27, no. 1, pp. 99-107, June 2018.
