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. †arvind_974@indiatimes.com