A Note on Fourth Order Method for Doubly Singular Boundary Value Problems

We present a fourth order finite difference method for doubly singular boundary value problem p x y′ x ′ q x f x, y , 0 < x ≤ 1 with boundary conditions y 0 A or y′ 0 0 or limx→ 0p x y′ x 0 and αy 1 βy′ 1 γ , where α > 0 , β ≥ 0 , γ and A are finite constants. Here p 0 0 and q x is allowed to be discontinuous at the singular point x 0. The method is based on uniform mesh. The accuracy of the method is established under quite general conditions and also corroborated through one numerical example.