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

Abstract

The fourth-order finite difference method developed by M. M. Chawla (M. M. Chawla, A fourth-order finite-difference method based on uniform mesh for singular two-point boundary-value problems, J. Comput. Appl. Math., 17 (1987) 359–364.) based on uniform mesh for the singular two-point boundary value (BV) problems

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

The order of the method has been established for general function p(x) and under quite general conditions on f(x, y). Numerical examples for general function p(x) verify the order of convergence of the method.

^†[email protected]

Keywords:

• Two-point singular boundary value problems
• Finite difference method
• Uniform mesh

Acknowledgments

This work is supported by Department of Science and Technology, New Delhi, India and Council of Scientific and Industrial Research, New Delhi, India.

Notes

^†[email protected]