Approximation of Higher-order Singular Initial and Boundary Value Problems by Iterative Decomposition and Bernstein Polynomial Methods

In very recent time, various works have focused on the analysis of Singular Boundary Value Problems, with many techniques developed or used to deal with major questions relating to Singular Initial and Boundary Value Problems and their solutions. The main questions relate to existence and uniqueness of solution, the numerical approximation of solutions and convergence of solutions.
In this work, we focus on the last two questions for some classes of Singular Initial and Boundary Value Problems. We developed two approximation methods namely Iterative Decomposition and Bernstein Polynomial Methods and applied them to tackle the last two questions raised in this work.
Some numerical examples of second, third and fourth orders problems are considered to illustrate the efficiency and accuracy of the methods.