Numerical Proceduers for Computing the Exact Solutions to Systems of Ordinary Differential Equations

Nidal Anakira^{1, 2,*}, Osama Oqilat³, Adel Almalki⁴, Irianto Irianto⁵, Saad Meqdad⁶, Ala Amourah¹

¹Faculty of Education and Arts, Mathematics Section, Sohar University,Sohar 3111, Sultanat  of Oman

²Jadara University Research Center, Jadara University, Jordan

³Department of Basic Sciences, Faculty of Arts and Science, Al-Ahliyya Amman University, Amman 19328, Jordan

⁴Department of Mathematics, Al-Qunfudhah University College, Umm Al-Qura University, Mecca, Saudi Arbia

⁵Department General Education, Faculty of Resilience, Rabdan Academy, Abu Dhabi 22401, United Arab Emirates

⁶Applied Science Private University, Amman, Jordan
Email:  nanakira@su.edu.om; o.oqilat@ammanu.edu.jo; aaamalki@uqu.edu.sa; iharny@ra.ac.ae; s_meq75@yahoo.com; AAmourah@su.edu.om

Abstract

This paper presents a modified homotopy perturbation method (HPM), which aimed at solving systems of ordinary differential equations (ODEs). The MHPM, which combines the HPM, Laplace transform, and Padé approximants, offers an alternative approach to address the challenges associated with solving such problems. By employing this method, it becomes feasible to overcome these challenges and obtain a dependable approximation for the exact solution. The effectiveness and applicability of the proposed scheme are demonstrated through preliminary results derived from illustrative examples, all of which correspond to exact solutions.

Keywords: Numerical Approximation; HPM; MHPM; Laplace transformation; Padé approximants