On the Convergence of Finite Difference Method for General Singular Boundary Value Problems

Abstract

The finite difference method M₃ developed in Ref. [4] by Chawla and Katti for singular two point boundary value problems

with p(x) = x ^{b ₀} , 0 ≤ b ₀ < 1 and boundary conditions y(0) = A, y(1) = B (A, B are constants) has been extended for the singular boundary value problems with general function p(x) = x ^{b ₀} g(x), 0 ≤ b ₀ < 1 and the boundary conditions

Second order convergence of the method has been established for quite general conditions. Numerical examples for general function p(x) verify the order of convergence of the method.

Keywords:

• 2 point singular B.V. problems
• Finite difference method

Acknowlegement

This work is supported by Department of Science and Technology, New Delhi, India and CSIR, New Delhi, India.