An Examination of a Second Order Numerical Method for Solving Initial Value Problems

  • S. E. Fadugba Department of Mathematics, Ekiti State University, Ado Ekiti, Ekiti State
  • S. N. Ogunyebi Department of Mathematics, Ekiti State University, Ado Ekiti, Ekiti State
  • B. O. Falodun Department of Mathematics, University of Ilorin, Kwara State
Keywords: Accuracy, exact solution, initial value problem, stability

Abstract

This paper presents an examination of a Second Order Convergence Numerical Method (SOCNM) for solving Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs). The SOCNM has been derived via the interpolating function comprises of polynomial and exponential forms. The analysis and the properties of SOCNM were discussed. Three numerical examples have been solved successfully to examine the performance of SOCNM in terms of accuracy and stability. The comparative study of SOCNM, Improved Modified Euler Method (IMEM), Fadugba and Olaosebikan Scheme (FOS) and the Exact Solution (ES) is presented. By varying the step length, the absolute relative errors at the final nodal point of the associated integration interval are computed. Furthermore, the analysis of the properties of SOCNM shows that the method is consistent, stable, convergent and has second order accuracy. Moreover, the numerical results show that SOCNM is more accurate than IMEM and FOS and also compared favourably with the ES. By varying the step length, there are two-order decrease in the values of the final absolute relative errors generated via SOCNM. Hence, SOCNM is found to be accurate, stable and a good tool for the numerical solutions of IVPs of different characteristics in ODEs.

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Published
2020-08-01
How to Cite
Fadugba, S. E., Ogunyebi, S. N., & Falodun, B. O. (2020). An Examination of a Second Order Numerical Method for Solving Initial Value Problems. Journal of the Nigerian Society of Physical Sciences, 2(3), 120-127. https://doi.org/10.46481/jnsps.2020.92
Section
Original Research