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.

Automated summary

In this work, a powerful method for solving non-linear singular boundary value problems, known as the advanced Adomian decomposition method, is introduced. This method discusses the use of boundary conditions to obtain coefficient of approximate series solution, provides convergence analysis, error bound, and illustrates high precision approximations with a large effective region of convergence. Examples are considered to demonstrate the robustness and effectiveness of the proposed method.