Author : Muhammad Nadeem, Afifa Maqsood, Muhammad Moaz Safer, Hira Fatima, Abdul Raheem and Tazeem Fatima

In this research work, the approximate solutions for nonlinear singular initial value problems are to be calculated by using modified Laplace decomposition (MLDM). The modified Adomian decomposition method and Homotopy perturbation methods are to be used to calculate the approximate solutions for the same problem. Moreover, the convergence analysis and the error found for the approximate solution are to be discussed. To prove the robustness and effectiveness of the proposed method, several examples are to be considered and the results calculated in this way will be compared with those obtained from other two above mentioned method. The time consuming behaviour of these method will be noted in order to check the simplicity, accuracy and efficiency of method.

Keywords: Initial Value Problems, Boundary Value Problems, Modified Laplace Decomposition Method, Homotopy Perturbation Method. He,s polynomials.