Euler-Maclaurin Method for Approximating Solutions of Initial Value Problems
(1) Mohammad W. Alomari Mail (Jadara University, Jordan)
(2) * Iqbal M. Batiha Mail (1) Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan. 2) Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates)
(3) Wala’a Ahmad Alkasasbeh Mail (Al Zaytoonah University of Jordan, Jordan)
(4) Nidal Anakira Mail (1) Faculty of Education and Arts, Sohar University, Sohar 3111, Oman. 2) Applied Science Research Center, Applied Science Private University, Amman 11937, Jordan)
(5) Iqbal H. Jebril Mail (Al Zaytoonah University of Jordan, Jordan)
(6) Shaher Momani Mail (1) Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates. 2) Department of Mathematics, The University of Jordan, Amman, Jordan)
*corresponding author

Abstract


This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms Taylor’s and Runge–Katta’s methods in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Taylor and Runge-Katta methods. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods.

Keywords


Euler-Maclaurin Formula; Euler Method; Darboux’s Formula; Approximations; Initial Value Problem

   

DOI

https://doi.org/10.31763/ijrcs.v5i1.1560 		      

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