Numerical Soluion of Singular Initial Value Problems in Ordinary Differential Equations by Iterative Decomposition and Bernstein Polynomial Methods

Over the years, analysis of Singularly Boundary Value Problems have been achieved by applying various methods and or techniques. Fundamental issues have been on the existence and uniqueness of solutions, as well as approximation of solutions when they exist. In this work, the solution of certain classes of Singular Initial and Boundary Value Problems are approximated using the Iterative Decomposition Method and the Bernstein Polynomials Method. Solutions are presented in each case as easily computable terms of an infinite convergent series. Numerical examples are given to establish the efficiency and accuracy of the proposed methods.