An Efficient Analytical Method for Solving Singular Initial Value Problems of Nonlinear Systems

Authors

Iryna Komashynska, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanFollow
Mohammed Al-Smadi, Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, JordanFollow
Omar Abu Arqub, Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanFollow
Shaher Momani, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan\\ Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Kingdom of Saudi ArabiaFollow

Author Country (or Countries)

Kingdom of Saudi Arabia

Abstract

The aim of the present analysis is to apply a relatively recent method, the residual-power series method (RPSM), in order to obtain efficient analytical numerical solutions for a class of nonlinear systems of initial value problems with finitely many singularities. The solution methodology provided the analytical solutions in terms of a rapidly convergent series with easily computable components. This novel approach possesses main advantage as compared to other exiting methods; it reproduces exact form when the solution is polynomial without linearization or perturbation; it can be applied without any limitation on the nature of the problem, type of classification, and the number of mesh points. Numerical experiments are discussed quantitatively to illustrate the theoretical statements and to show potentiality, superiority, and applicability of the proposed technique for solving such nonlinear singular system of differential equations. The results demonstrate reliability and efficiency of the technique developed.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100224

Recommended Citation

Komashynska, Iryna; Al-Smadi, Mohammed; Abu Arqub, Omar; and Momani, Shaher (2016) "An Efficient Analytical Method for Solving Singular Initial Value Problems of Nonlinear Systems," Applied Mathematics & Information Sciences: Vol. 10: Iss. 2, Article 24.
DOI: http://dx.doi.org/10.18576/amis/100224
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss2/24