On the convergence of second-order finite difference method for weakly regular singular boundary value problems

Abstract

The second-order finite difference method developed by Chawla and Katti in 1985 based on a uniform mesh for the singular two-point boundary value problems

with , 0≤b ₀<1 and boundary conditions y(0)=A, y(1)=B (A, B are finite constants) has been extended for general class of non-negative functions , 0≤b ₀<1 and the boundary conditions

Second-order convergence of the method has been established for general non-negative function p(x) and under quite general conditions on f(x, y). Our method is based on one evaluation of f and for p(x)=1, it reduces to the classical second-order method for y′′ = f(x, y). In the case of , 0≤b ₀<1, this method provides better results than some existing second-order method which is corroborated by one example, and the order of method is also corroborated for general non-negative functions p(x).

Keywords:

• finite difference
• two-point singular B. V. problems
• uniform mesh

2000 AMS Subject Classification :

• 65L10

CCS Category :

• G1.7

Acknowledgements

This work is supported by National Board for Higher Mathematics, Department of Atomic Energy, Mumbai, India. The author is also thankful to the referees for thier valuable comments and suggestions.