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

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 Pad approximation (PA) of order compared with the exact solution.