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A uniform mesh finite difference method for a class of singular two-point boundary value problems. (English) Zbl 1103.65088

Summary: A method is described based on a uniform mesh for the class of singular two-point boundary value problems \[ (x^\alpha y')'=f(x,y),\;0<x \leq 1, y(0)=A,\;y(1)=B. \] It is shown to be order \(h^4\) convergent for all \(\alpha\in(0,1)\).

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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