On the convergence of finite difference methods for a class of two-point boundary value problems with periodic boundary conditions
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In this paper we present a detailed convergence analysis to establish second-order convergence for a three-point two parameter family of finite difference methods (based on one evaluation of f) for the class of two-point boundary value problems (TPBVPs) y″+f(x,y)=o, o⩽x⩽1y(o)=y(1), y′(o)=y′(1) under suitable conditions on ∂f/∂y and for y ϵ C4[0,1]. Some numerical examples are provided to illustrate the results.
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论文评审过程:Available online 28 April 2003.
论文官网地址:https://doi.org/10.1016/0096-3003(96)90073-9