International Council for Education, Research and Training

A-4 Step Chebyshev Based Multiderivative Direct Solver For Third Order Ordinary Differential Equations

Ogunlaran, O.M1

1Mathematics Programme, College of Agriculture, Engineering and Science, Bowen University, Iwo, Osun State, Nigeria.

Kehinde, M.A2

2Department of Mathematics, Federal College of Education (Special), Oyo, Nigeria.

Abstract

This paper develops and examines a uniform order, 4 step block method with Chebyshev series as bases function. Collocation and interpolation technique was used to modeled implicit discrete schemes from continuous scheme to derive our block. The block method obtained was of order 4. It is consistent, zero stable and consequently zero stable.  The results obtained from four test problems shown that the method converges to exact solutions and perform better than some existing methods in the literatures.

Keywords: Multiderivative, Chebyshev series, Continuous Scheme, Direct solver.

Impact statement

This research presents a novel 4-step Chebyshev-based method for solving third-order ordinary differential equations (ODEs), offering an efficient and accurate approach for tackling complex problems in various fields, such as physics, engineering, and applied mathematics. The proposed method:

 

– Improves accuracy by utilizing Chebyshev polynomials to approximate solutions

– Provides a reliable and robust tool for solving third-order ODEs, which are commonly encountered in modeling real-world phenomena

 

The impact of this research is two fold:

1. Advancements in numerical analysis: This method contributes to the development of more efficient and accurate numerical techniques for solving ODEs, pushing the boundaries of computational mathematics.

2. Practical applications: The proposed method can be applied to various fields, such as:

– Physics: Modeling complex systems, like chaotic dynamics or quantum mechanics

– Engineering: Optimizing systems, like control systems or electronic circuits

– Applied mathematics: Solving problems in fluid dynamics, thermodynamics, or biomechanics

 
About the Author

Prof. O.M. Ogunlaran is a Professor of Numerical Analysis at  Mathematics ProgramCollege of Agriculture, Engineering and Science of Bowen University, Iwo, Nigeria. He decades of experience in teaching of applied Mathematics at various levels of degree. He has supervised several 1st degree, M.Sc and Ph.D students in Numerical Analysis. He has several international and national conferences experience and publications to his credit.

 

Dr. M.A. Kehinde is Ph.D holder of Numerical Analysis. He is a teaches Mathematics and Mathematics education at both NCE and degree level at Federal College of Education (Special), Oyo. He has several international and national conferences and publications

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