Archive
Special Issues Volume 6, Issue 2, June 2020, Page: 13-31
A Step by Step Guide on Derivation and Analysis of a New Numerical Method for Solving Fourth-order Ordinary Differential Equations
Ezekiel Olaoluwa Omole, Department of Mathematics & Statistics, College of Natural Sciences, Joseph Ayo Babalola University, Osogbo, Nigeria
Luke Azeta Ukpebor, Department of Mathematics, Faculty of Physical Sciences, Ambrose Alli University, Ekpoma, Nigeria
Received: Apr. 25, 2020;       Accepted: May 18, 2020;       Published: Sep. 23, 2020
Abstract
This manuscript presents a step by step guide on derivation and analysis of a new numerical method to solve initial value problem of fourth order ordinary differential equations. The method adopted hybrid techniques using power series as the basic function. Collocation of the fourth derivatives was done at both grid and off-grid points. The interpolation of the approximate function is also taken at the first four points. The complete derivation of the new technique is introduced and shown here, as well as the full analysis of the method. The discrete schemes and its first, second, and third derivatives were combined together and solved simultaneously to obtain the required 32 family of block integrators. The block integrators are then applied to solve problem. The method was tested on a linear system of equations of fourth order ordinary differential equation in order to check the practicability and reliability of the proposed method. The results are displaced in tables; it converges faster and uses smaller time for its computations. The basic properties of the method were examined, the method has order of accuracy p=10, the method is zero stable, consistence, convergence and absolutely stable. In future study, we will investigate the feasibility, convergence, and accuracy of the method by on some standard complex boundary value problems of fourth order ordinary differential equations. The extension of this new numerical method will be illustrated and comparison will also be made with some existing methods.
Keywords
Derivation, Analysis, Fourth-order Ordinary Differential Equations, New numerical Method, Hybrid Techniques, Convergence, Zero Stability, Consistency, Taylor Series, Order 10, Integrators
Ezekiel Olaoluwa Omole, Luke Azeta Ukpebor, A Step by Step Guide on Derivation and Analysis of a New Numerical Method for Solving Fourth-order Ordinary Differential Equations, Mathematics Letters. Vol. 6, No. 2, 2020, pp. 13-31. doi: 10.11648/j.ml.20200602.12
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