Four-Step One Hybrid Block Methods for Solution of Fourth Derivative Ordinary Differential Equations

Raymond, Dominic; Skwame, Yusuf; Adiku, Lydia

doi:10.9734/jamcs/2021/v36i330343

Submit Manuscript

Subscription

Four-Step One Hybrid Block Methods for Solution of Fourth Derivative Ordinary Differential Equations

Raymond, Dominic

Skwame, Yusuf

Adiku, Lydia

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2021/v36i330343
Published: 8 April 2021

Abstract

We consider developing a four-step one offgrid block hybrid method for the solution of fourth derivative Ordinary Differential Equations. Method of interpolation and collocation of power series approximate solution was used as the basis function to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and said to be converge. The developed four-step method is applied to solve fourth derivative problems of ordinary differential equations from the numerical results obtained; it is observed that the developed method gives better approximation than the existing method compared with.

Keywords:

Four-step
hybrid point
fourth derivative
power series
ODE’s
interpolation

How to Cite

Dominic, R., Yusuf, S., & Lydia, A. (2021). Four-Step One Hybrid Block Methods for Solution of Fourth Derivative Ordinary Differential Equations. Journal of Advances in Mathematics and Computer Science, 36(3), 1-10. https://doi.org/10.9734/jamcs/2021/v36i330343

References

Kayode SJ, Obuarhua FO. Continuous y-function hybrid methods for direct solution of differential equations. Intern. J. of Differential Equations and Application. 2013;12:37-48.

James A, Adesanya A, Joshua S. Continuous block method for the solution of second order initial value problems of ordinary differential equation. Int. J. Pure Appl. Math. 2013;83:405-416.

Awoyemi DO. Algorithmic collocation methods for direct solution of special and general fourth order initial value problems in ordinary differential equations. Intern Journal of Computer Math. 2001;6: 271-218.

Awoyemi DO, Kayode SJ. An optimal order continuous multistep algorithm for initial value of special second order differential equations. Journal of the Nigeria Association of Mathematical Physics. 2002;6:285-292.

Awoyemi DO. A P-stable linear multistep method for solving general third order Ordinary Differential Equations. International Journal of Computer Mathematics. 2003;80(8):978-993.

Awoyemi DO. Algorithm Collocation approach for direct solution of fourth order initial value problems of ordinary differential equations. Int. J. Comput Math. 2005;82(3):321-329. Available:https://doi.org/10.1080/00207160412331296634

Adeyeye O, Omar Z. New self starting approach for solving special third order initial value problems. International Journal of Pure and Applied Mathematics. 2018;118(3):511-517.

Adeyeye O, Kayode SJ. Two-step two-point hybrid method for general second order differential equations. Afr. J. Math. Comput. Sci. Res. 2013;6(10):191-196. Available:https://doi.org/10.5897/AJMCSR2013.0502

Kayode SJ. An order six zero stable method for direct solution of fourth order ordinary differential equations. Am J. Appl Sci. 2008;5(11):1461-1466.

Jator SN. Numerical integrators for fourth order initial and boundary value problems. Int J. Pure Appl. Math. 2008;47(4):567-576.

Jator SN, Lee L. Implementing a seventh-order linear multistep method in a predictor-corrector mode or block mode, which is more efficient for general second order initial value problems. Springer Plus. 2014;3(1):1-8. Available:https://doi.org/10.1186/2193-1801-3-447.

Waeleh N, Majid ZA, Ismail F, Sulieman M. Numerical solution of higher order ordinary differential equations by direct block code. Journal of Mathematics and Statistics. 2011;8(1):77-81.

Adeyeye O, Omar Z. Implicit five-step Block Method with Generalised Equidistant points for Solving Fourth Order Linear and non-Linear Initial Value Problems. Ain Shams Engineering Journal. 2019;10:881-889.

Adeyeye O, Omar Z. Solving fourth order linear initial and boundary value problems using an implicit block method. Proceedings of the third international conference on computing mathematics and statistics (iCMS2017); 2019. Available:https://doi.org/10.1007/978-981-13-7279-7_21

Lee KP, Fudziah I. Block hybrid collocation method with application to fourth order differential equations. Hindawi Publishing Corporation Mathematical Problems in Engineering. 2014;2015Article ID 561489:6. Available:https://doi.org/10.1155/2015/561489

Akinfenwa OA, Ogunseye HA, Okunuga SA. Block hybrid method for solution of fourth order ordinary differential equations. Nigerian Journal of Mathematics and Applications. 2016;25:146-150.

Adoghe LO, Omole EO. A two-step hybrid block method for the numerical integration of higher order initial value problems of ordinary differential equations. An International Scientific Journal. 2019;118:236-250.

59 times
32 times

Download Statistics

Downloads

Download data is not yet available.