Procedure for Exact Solutions of Stiff Ordinary Differential Equations Systems
Brahim Benhammouda
Abu Dhabi Men's College, Higher Colleges of Technology, P.O. Box 25035, Abu Dhabi, United Arab Emirates.
Hector Vazquez-Leal *
Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltran S/N, C.P. 91000, Xalapa, Veracruz, México.
L. Benhamouche
Department of Mathematics, University of Blida, Algeria.
H. Zahed
Department of Mathematics, Taibah University, P.O. Box 30002 Al Madina Al Munawwarah, Saudi Arabia.
Y. Abo Einaga
Department of Mathematics, Taibah University, P.O. Box 30002 Al Madina Al Munawwarah, Saudi Arabia.
A. Sarmiento-Reyes
National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro #1, Sta. Mara Tonantzintla 72840, Puebla, México.
A. Marin-Hernandez
Department of Articial Intelligence, Universidad Veracruzana, Sebastian Camacho No. 5 Centro, 91000, Xalapa, Veracruz, México.
J. Huerta-Chua
Faculty of Civil Engineering, University Veracruzana, Venustiano Carranza S/N, Col. Revolucion, 93390, Poza Rica, Veracruz, México.
*Author to whom correspondence should be addressed.
Abstract
In this work, we present a technique for the analytical solution of systems of sti ordinary dierential equations (SODEs) using the power series method (PSM). Three SODEs systems are solved to show that PSM can nd analytical solutions of SODEs systems in convergent series form. Additionally, we propose a post-treatment of the power series solutions with the Laplace-Pade (LP) resummation method as a powerful technique to nd exact solutions. The proposed method gives a simple procedure based on a few straightforward steps.
Keywords: Sti ordinary dierential equations, Power series method, Laplace transform, Pade approximant, Analytical solutions.