Adam-Bash forth-Multan Predictor Corrector Method for Solving First Order Initial value problem and Its Error Analysis
Article Sidebar
Main Article Content
Abstract
This paper presents fourth order Adams predictor corrector numerical scheme for solving initial value problem. First, the solution domain is discretized. Then the derivatives in the given initial value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of difference equations is developed. The starting points are obtained by using fourth order Runge-Kutta method and then applying the present method to finding the solution of Initial value problem. To validate the applicability of the method, two model examples are solved for different values of mesh size. The stability and convergence of the present method have been investigated. The numerical results are presented by tables and graphs. The present method helps us to get good results of the solution for small value of mesh size h. The proposed method approximates the exact solution very well. Moreover, the present method improves the findings of some existing numerical methods reported in the literature.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
How to Cite
References
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, 5, 393-404 (2015). [CrossRef]
Islam MA. Accuracy Analysis of Numerical solutions of initial value problems (IVP) for ordinary differential equations (ODE). IOSR Journal of Mathematics. 2015;11(3):18-23.
Islam, Md.A. Accurate Solutions of Initial Value Problems for Ordinary Differential Equations with Fourth Order Runge Kutta Method. Journal of Mathematics Research.7,41-45,(2015). [CrossRef]
Ogunrinde, R.B., Fadugba, S.E. and Okunlola, J.T. On Some Numerical Methods for Solving Initial Value Problems in Ordinary Differential Equations. IOSR Journal of Mathematics, 1, 25-31,(2012) [CrossRef]
Eaqub Ali SM. A Text Book of Numerical Methods with Computer Programming. Beauty Publication, Khulna. 2006.
Akanbi, M.A. Propagation of Errors in Euler Method, Scholars Research Library. Archives of Applied ScienceResearch,2,457-469,(2010).
Kockler, N. “Numerical Method for Ordinary Systems of Initial value Problems.” (1994).
Lambert, John D. "Computational methods in ordinary differential equations." (1973).
Gear, C. William. "Numerical initial value problems in ordinary differential equations." nivp (1971).
Hall, George, and James Murray Watt, eds. Modern numerical methods for ordinary differential equations. Oxford University Press, 1976. 11. Hossain, Md Babul, Md Jahangir Hossain, Md Musa Miah, and Md Shah Alam. "A comparative study on fourth order and butcher’s fifth order runge-kutta methods with third order initial value problem (IVP)." Applied and Computational Mathematics 6, no. 6 (2017): 243-253. [CrossRef]
Hossen, Murad, et al. "A comparative Investigation on Numerical Solution of Initial Value Problem by Using Modiffied Euler Method and Runge Kutta Method." ISOR Journal of Mathematics (IOSR-JM) e-ISSN (2019): 2278-5728.
Singh, Neelam. "Predictor Corrector Method of Numerical analysis-New Approach." International Journal of Advanced Research in Computer Science 5, no. 3 (2014).
Sastry, Shankar S. Introductory methods of numerical analysis. PHI Learning Pvt. Ltd., 2012.
Burden, R. L. "FairesJD: Numerical Analysis." New York: Prindle, Weber & Schmidt (1985).
Hossen, Murad, Zain Ahmed, Rashadul Kabir, and Zakir Hossan. "Acomparative Investigation on Numerical Solution of Initial Value Problem by Using Modiffied Euler Method and Runge Kutta Method." ISOR Journal of Mathematics (IOSR-JM) e-ISSN (2019): 2278-5728.
Hossain, Md Jahangir, Md Shah Alam, and Md Babul Hossain. "A stdy on the Numerical Solutions of Second Order Initial Value Problems (IVP) for Ordinary Differential Equations with Fourth Order and Butcher’s Fifth Order Runge-Kutta Methods." American Journal of Computational and Applied Mathematics 7, no. 5 (2017): 129-137.
Inyengar S.R..K and Jain R.K. Numerical Method. New Age International (P) Ltd, New Delhi,(2009).
Emmanuel, Fadugba Sunday, Adebayo Kayode James, Ogunyebi Segun Nathaniel, and Okunlola Joseph Temitayo. "Review of Some Numerical Methods for Solving Initial Value Problems for Ordinary Differential Equations." International Journal of Applied Mathematics and Theoretical Physics 6, no. 1 (2020): 7. [CrossRef]
Griffiths DF, Higham DJ. Numerical methods for ordinary differential equations: initial value problems. Springer Science & Business Media; (2010). [CrossRef]
Iserles A. Numerical solution of differential equations, by MK Jain. Pp 698.£ 17· 95. 1984. ISBN 0-85226-432-1 (Wiley Eastern). The Mathematical Gazette. 1985 Oct;69(449):236-7. [CrossRef]