On the Simulation of Higher Order Linear Block Algorithm for Modelling Fourth Order Initial Value Problems
Asian Research Journal of Mathematics,
The introduction of new linear block method for the direct simulation of fourth order IVPs has been developed in this article. The reason for adopting direct simulation of fourth order initial value problems is to address some setbacks in reduction method. When developing the method, we adopted the linear block approach through a one step method. We have validated the accuracy of the method on some fourth order initial value problems without reduction process, and the results are better than the conventional method. The numerical experiments were given and the results obtained were found to be better in accuracy than the existing methods in literature.
- Linear block Approach
- fourth order
- numerical experiment
How to Cite
Omole EO. Some implicit hybrid Numerov type block methods for direct solution of fourth order ordinary differential equations. M.Tech Thesis, Federal University of Technology, Akure, Ondo State, Nigeria. 2016;1-250.
Cortell R. Application of the fourth-order Runge-Kutta method for the solution of high-order general initial value problems. Comput. Struct. 1993;49:897-900.
Sabo J, Kyagya TY, Solomon S. One-step hybrid block scheme for the numericalapproximation for solution of third order initial value problems. Journal of Scientific Research & Reports. 2021;27(12):51-61.
Hussain K, Ismail F, Senu N. Two embedded pairs of Runge-Kutta type methods for direct solution of special fourth-order ordinary differential equations. Math. Prob. Eng. 2015;1–12.
Oluwaseun A, Zurni O. A new algorithm for developing block methods for solving fourth order ordinary differential equations. Global Journal of Pure and Applied Mathematics. 2016;12:1465-1471.
Kuboye JO, Omar Z. New zero-stable block method for direct solution of fourth order ordinary differential equations. Indian Journal of Science and Technology. 2015;8(12):1-8.
Ukpebor LA, Omole EO, Adoghe LO. An order four numerical scheme for fourth-order initial value problems using lucas polynomial with application in ship dynamics. International Journal of Mathematical Research. 2020;9(1):28-41.
Familua AD, Omole EO. Five points mono hybrid point linear multistep method for solving nth order ordinary differential equations using power series function. Asian Research Journal of Mathematics. 2017;3(1):1-17.
Ahamad N, Charan S. Study of numerical solution of fourth order ordinary differential equations by fifth order Runge-Kutta method. Int. J. Sci. Res. Sci. Eng. Technol. 2019;6(1):230-237.
Adeyeye A, 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.
Kayode SJ. An efficient zero-stable numerical method for fourth-order ordinary differential equations. Inter. J. Mathematics and Mathematical Sciences. 2008;1155- 1165.
Awoyemi DO, Kayode SJ, Adoghe O. A Six-step continuous multistep method for the solution of general fourth order initial value problems of ordinary differential equations. J. Nat. Sci. Res. 2015;5:131–138.
Yap L, Ismail F. Block hybrid collocation method with application to fourth order differential equations. Math. Probl. Eng. 2015;1–6.
Abstract View: 83 times
PDF Download: 52 times