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^b₀, 0 ≤ b₀ < 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^b₀g(x), 0 ≤ b₀ < 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.†

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