Adomian decomposition method for solving derivative-dependent doubly singular boundary value problems

TL;DR

This paper introduces a modified Adomian decomposition method utilizing a new two-fold integral operator to effectively solve nonlinear derivative-dependent doubly singular boundary value problems, demonstrated through three examples.

Contribution

The work presents a novel modification of the ADM with a new integral operator for solving complex singular boundary value problems.

Findings

Accurate approximate solutions obtained for three example problems.

Numerical results show good agreement with known solutions.

Method proves efficient for nonlinear derivative-dependent singular problems.

Abstract

In this work, we apply Adomian decomposition method for solving nonlinear derivative-dependent doubly singular boundary value problems: $(py')'= qf(x,y,y')$. This method is based on the modification of ADM and new two-fold integral operator. The approximate solution is obtained in the form of series with easily determinable components. The effectiveness of the proposed approach is examined by considering three examples and numerical results are compared with known results.