https://doi.org/10.1140/epjp/s13360-024-05762-3
Regular Article
Limit residual function method and applications to PDE models
1
Department of Mathematics, Faculty of Science, Al Balqa Applied University, 19117, Salt, Jordan
2
Department of Mathematics, Faculty of Science, Zarqa University, 13110, Zarqa, Jordan
Received:
5
May
2024
Accepted:
20
October
2024
Published online:
5
November
2024
The article focuses on finding analytical series solutions for linear and nonlinear partial differential equations. It introduces a new technique named the limit residual function method, which is used to determine the coefficients of the power series solution of the equations. This method does not require transforming the target equation into another space and rely on the concept of the limit and the residual function. The article discusses various applications to demonstrate the proposed method’s effectiveness, reliability, and ease. These applications cover five types of partial differential equations: Navier–Stokes, reaction–diffusion, Fisher, Klein-Gordon, Poisson, and Hunter–Saxton equations.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
