The differential-difference equation  is a special case of the pantograph equation  at  The pantograph is the device responsible for gathering the current in electric trains. The present paper develops an ansatz method to solve the current model. The developed ansatz method is capable to obtain the solution in exact wave form which has not been reported in the literature. At special cases of the involved parameters, the obtained exact solutions are in full agreement with the corresponding ones in the literature via a series approach. However, the present method is direct, simpler, and can be further extended to include other complex models of the same type.

ansatz method, differential-difference equation, pantograph, exact solution.

Received: November 2, 2022; Accepted: December 14, 2022; Published: December 29, 2022

How to cite this article: Weam G. Alharbi, Solution of a differential-difference equation via an ansatz method, Advances and Applications in Discrete Mathematics 36 (2023), 55-68. http://dx.doi.org/10.17654/0974165823004

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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