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The Zeros of Real Life Problems by Some One-Step Methods Represented in Ordinary Differential Equation (Ode)
Current Issue
Volume 6, 2018
Issue 4 (December)
Pages: 29-36   |   Vol. 6, No. 4, December 2018   |   Follow on         
Paper in PDF Downloads: 29   Since Jan. 17, 2019 Views: 685   Since Jan. 17, 2019
Authors
[1]
Fola John Adeyeye, Department of Mathematics/Computer Science, College of Science, Federal University of Petroleum Resources, Effurun, Nigeria.
[2]
Garen Omonigho, Department of Mathematics/Computer Science, College of Science, Federal University of Petroleum Resources, Effurun, Nigeria.
Abstract
The Runge-kutta scheme which is a one-step method remains one of the most versatile Numerical schemes used in the solution of Initial value problem(IVP) in the real world of Engineering, Biological and Social sciences more especially some stiff problems. In this Paper we present some One-step schemes such as Euler’s (RK1) Heun’s Method (RK2) Runge-kutta of IV (RK4) and Runge-kutta of V (RK5) for the unique solutions of some problems in ordinary differential equation. The performance of these methods was critically analyzed at various stages of mesh points (h) with respect to difference methods. The performance of h of different method provide a convincing superiority, uniqueness, efficiency as well as the theoretical stability of each method to the solution of Initial value problems in ode. This was carefully achieved by the schemes or methods satisfying the uniqueness, consistence and stability condition. A computational numerical comparism on each table shows that at given an adjusted step size h, to the advantage backward Euler’s method (h/4) Heun’s method with a step size (h/2), RK4 and RK5 methods still perform and produce better and stable results as they converge to the exact solution.
Keywords
IVP, Real Life Problems, One-Step Methods (Runge-Kutta of Orders I II, IV and V)
Reference
[1]
M. A. Islam. (2015).“A Comparative Study On Numerical Solutions Of Initial Value Problems (IVP) For Ordinary Differential Equations (ODE) With Euler And Runge-Kutta Methods”. American Journal of Computational Mathematics, Vol. 5, pp. 393–404.
[2]
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