Combining Laplace transform and Adomian decomposition method for solving singular IVPs of Emden-Fowler of partial differential equations

• Published in: AL-Rafidain journal of computer sciences and mathematics Vol. 17; no. 2; pp. 79 - 92
• Main Authors: Al-Hayani, Waleed, Yassin, Fatima
• Format: Journal Article
• Language: Arabic; English
• Published: Mosul University 23-12-2023
• Subjects: adomian decomposition method; adomian polynomials; emden-fowler equation; laplace transform method; wave-type equation
• ISSN: 2311-7990; 1815-4816; 2311-7990
• DOI: 10.33899/csmj.2023.181634

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.