Laplace-Adomian Decomposition Method for solving higher-Order Pantograph-Type Delay Differential Equations

Year 2025, Volume: 3 Issue: 2, 78 - 89, 16.12.2025

Adedapo Alaje , Moruf Oyedunsi Olayiwola

https://doi.org/10.26650/ijmath.2025.00030

https://izlik.org/JA44YX32MF

Abstract

The high-order pantograph-type delay differential equations represent a model for the dynamics of electric trains with respect to pantograph systems for power collection from overhead wires. Accurate solutions for these equations are of importance for engineers dealing with improvements in the pantograph design, wear forecasting, and maximization of efficiency in power transmission as well as minimizing mechanical stress in the pantograph and overhead wires. This paper applies the Laplace Adomian decomposition method to handle both linear and nonlinear higher-order pantograph equations with achievable accurate solutions. The numerical tabulations and graphical illustrations demonstrate that this method is very efficient, accurate, and particularly easy to apply, and they therefore open up prospects for working on problems of a similar type.

Keywords

Delay differential equation (DDE) , Higher order Pantograph DDE , Laplace Adomian decomposition method

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