A fourth-order finite difference method based on uniform mesh for singular two-point boundary-value problems
We present a new fourth-order finite difference method based on uniform mesh for the (weakly) singular two-point boundary value problem: \((x^{\alpha}y')'=f(x,y)\), \(0<x\leq 1\), \(y(0)=A\), \(y(1)=B\), \(0<\alpha <1\). Our method provides \(O(h^ 4)\)-convergent approximations for all \(\alpha\in (0,1)\); for \(\alpha =0\) it reduces to the well-known fourth- order method of Numerov for \(y''=f(x,y)\).
singular two-point boundary value problem
scientific article; zbMATH DE number 3994955