Constructing series approximate solutions of ordinary differential equations using the limit residual function method
Authors
M. Abu Kharrob
- Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan.
A. Burqan
- Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan.
A. El-Ajou
- Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan.
Abstract
This article offers analytical solutions in power series form for ordinary differential equations. It provides an effective tool for deriving accurate analytical and numerical solutions to these equations via the use of a novel analytical approach called the limit residual function method. The suggested technique demonstrates that an exact solution can be found when a pattern exists in the obtained series solution; otherwise, only rough estimates can be provided. By comparing our results with exact solutions to the problems we discussed, we conclude that the present approach is simple, easy, and effective for solving differential equations, given that the consequent series approximate solutions are in the closed form of the actual results.
Share and Cite
ISRP Style
M. Abu Kharrob, A. Burqan, A. El-Ajou, Constructing series approximate solutions of ordinary differential equations using the limit residual function method, Journal of Mathematics and Computer Science, 41 (2026), no. 2, 195--206
AMA Style
Abu Kharrob M., Burqan A., El-Ajou A., Constructing series approximate solutions of ordinary differential equations using the limit residual function method. J Math Comput SCI-JM. (2026); 41(2):195--206
Chicago/Turabian Style
Abu Kharrob, M., Burqan, A., El-Ajou, A.. "Constructing series approximate solutions of ordinary differential equations using the limit residual function method." Journal of Mathematics and Computer Science, 41, no. 2 (2026): 195--206
Keywords
- Functional analysis
- ordinary differential equations
- power series
- residual function
MSC
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