Numerical solution of singular boundary value problems using advanced Adomian decomposition method

In this work, we present a powerful method for the numerical solution of non-linear singular boundary value problems, namely the advanced Adomian decomposition method which is the modification of the Adomian decomposition method. In this method, we use all the boundary conditions to obtain the coefficient of the approximate series solution. Moreover, convergence analysis and an error bound for the approximate solution are discussed. This method overcomes the singular behaviour of problems and illustrates the approximations of high precision with a large effective region of convergence. To prove the robustness and effectiveness of the proposed method, various examples are considered and the obtained results are compared with the other existing methods.