Development and analysis of a proposed scheme to solve initial value problems

Volume 26, Issue 3, pp 210--221 http://dx.doi.org/10.22436/jmcs.026.03.02

Publication Date: November 06, 2021 Submission Date: June 04, 2020 Revision Date: October 15, 2020 Accteptance Date: October 29, 2020

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Authors

S. E. Fadugba - Department of Mathematics, Ekiti State University, Ado Ekiti, Nigeria. et. al.

Abstract

This paper presents the development and analysis of a proposed scheme to solve Initial Value Problems (IVPs). The proposed scheme is devised by means of the interpolating function. The properties of the proposed scheme such as the local truncation error, order of accuracy, stability, consistency, and convergence are analyzed. Furthermore, the performance of the proposed scheme is tested on five numerical examples. Moreover, the comparative study of the results generated via the proposed scheme and the exact solution is presented. Hence, the proposed scheme has fifth order convergence and is a good tool for approximating the solution of IVPs.

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Keywords

• Consistency
• convergence
• error
• initial value problem
• stability

MSC

•  34A12
•  65L05
•  65L20
•  65L70

References

• [1] J. C. Butcher, Numerical methods for ordinary differential equations, Third Ed., John Wiley & Sons, Chichester (2016)
  • View Article
  • Google Scholar


• [2] S. E. Fadugba, An examination of the accuracy and zero stability of the explicit linear two-step method for initial value problems (IVPs) in ordinary differential equations (ODEs), Int. J. Sci. Res. Math. Stat. Sci., 7 (2020), 28--32
  • View Article


• [3] S. E. Fadugba, Development of an improved num erical integration method via the transcendental function of exponential form, J. Interdiscip. Math., 23 (2020), 1347--1356
  • View Article
  • Google Scholar


• [4] S. E. Fadugba, B. Falodun, Development of a new one-step scheme for the solution of initial value problem (IVP) in ordinary differential equations, Int. J. Theor. Appl. Math., 3 (2017), 58--63
  • View Article
  • Google Scholar


• [5] S. E. Fadugba, J. O. Idowu, Analysis of the properties of a third order convergence numerical method derived via transcendental function of exponential form, Int. J. Appl. Math. Theor. Phys., 5 (2019), 97--103
  • View Article
  • Google Scholar


• [6] S. E. Fadugba, S. N. Ogunyebi, B. O. Falodun, An examination of a second order numerical method for solving initial value problems, J. Niger. Soc. Phys. Sci., 2 (2020), 120--127
  • View Article
  • Google Scholar


• [7] S. E. Fadugba, J. T. Okunlola, Performance measure of a new one-step numerical technique via interpolating function for the solution of initial value problem of first order differential equation, World Sci. News, 90 (2017), 77--87
  • View Article
  • Google Scholar


• [8] S. E. Fadugba, T. E. Olaosebikan, Comparative study of a class of one-step methods for the numerical solution of some initial value problems in ordinary differential equations, Res. J. Math. Comput. Sci., 2 (2018), 1--11
  • Google Scholar


• [9] S. E. Fadugba, S. Qureshi, Convergent numerical method using transcendental function of exponential type to solve continuous dynamical systems, Punjab Univ. J. Math. (Lahore), 51 (2019), 45--56
  • View Article
  • MathSciNet


• [10] M .A. Islam, Accurate solutions of initial value problems for ordinary differential equations with fourth order Runge Kutta method, J. Math. Res., 41--45 (2015),
  • View Article
  • Google Scholar


• [11] M. K. Jain, S. R. K. Iyengar, R. K. Jain, Numerical Methods for Scientific and Engineering Computation, New Age International (P) Ltd., New Delhi (2003)
  • View Article
  • Google Scholar


• [12] J. D. Lambert, Computational methods in ordinary differential equations, John Wiley & Sons, London-New York-Sydney (1973)
  • MathSciNet
  • Google Scholar


• [13] R. B. Ogunrinde, S. E. Fadugba, Development of the new scheme for the solution of initial value problems in ordinary differential equations, Int. Organ. Sci. Res. J. Math., 2 (2012), 24--29
  • View Article
  • Google Scholar


• [14] S. Qureshi, S. E. Fadugba, Convergence of a numerical technique via interpolating function to approximate physical dynamical systems, J. Adv. Phys., 7 (2018), 446--450
  • View Article
  • Google Scholar


• [15] H. Ramos, G. Singh, V. Kanwar, S. Bhatia, Solving first-order initial-value problems by using an explicit non-standard A-stable one-step method in variable step size function, Applied Mathematics and Computation, New York (2015)
  • View Article
  • Google Scholar