A fourth-order finite difference method based on uniform mesh for singular two-point boundary-value problems

Abstract

We present a new fourth-order finite difference method based on uniform mesh for the (weakly) singular two-point boundary value problem: ( x α y′)′ = f( x, y), 0 < x ⩽ 1, y(0) = A, y(1) = B, 0 < α < 1. Our method provides O( h 4)-convergent approximations for all α ∈ (0, 1); for α = 0 it reduces to the well-known fourth-order method of Numerov for y″ = ƒ(x, y).