Adam-Bash forth-Multan Predictor Corrector Method for Solving First Order Initial value problem and Its Error Analysis
Kedir Aliyi Koroche1, Geleta Kinkino Mayu2
1Kedir Aliyi Koroche, Department of Mathematics, College of Natural and Computational Science, Ambo University, P.O.Box. 19, Ambo, Ethiopia.
2Geleta Kinkino Mayu, Department of Mathematics, College of Natural and Computational Science, Ambo University, P.O.Box. 19, Ambo, Ethiopia.
Manuscript received on 01 October 2021 | Revised Manuscript received on 10 October 2021 | Manuscript Accepted on 15 October 2021 | Manuscript published on 30 October 2021 | PP: 30-40 | Volume-1 Issue-2, October 2021 | Retrieval Number:100.1/ijam.B1112101221 | DOI: 10.54105/ijam.B1112.101221
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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.
Keywords: Initial Value Problem, Adams-Bashfor Method, Adams-Molten Method, Adamsbashfor-Molten, Stability, Convergence.
Scope of the Article: Applied Mathematics