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Keywords

Emden-Fowler Equation
Wave-type equation
Laplace Transform method
Adomian decomposition method
Adomian polynomials

Abstract

In this paper, the time-dependent Emden-Fowler type partial differential equations and wave-type equations with singular behavior at  are analytically solved using the combined Laplace transform and Adomain decomposition method (LT-ADM). To avoid the singularity behavior for both models at , the benefit of this single global technique is used to present a solid framework. The method is shown to produce approximate-exact solutions to various kinds of problems in One-dimensional space. The results gained in each case demonstrate the dependability and effectiveness of this approach. To show the high accuracy of the approximate solution results (LT-ADM), compare the absolute errors obtained by the Padé approximation (PA) of order compared with the exact solution.
https://doi.org/10.33899/csmj.2023.181634
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