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A class of simple exponential B-splines and their application to numerical solution to singular perturbation problems. (English) Zbl 0676.65088
The authors consider an application of simple exponential splines to the numerical solution of singular perturbation problem: \(\epsilon y''+b(x)y'-d(x)y=f(x),\) (0\(\leq x\leq 1)\), \(y(0)=\alpha\), \(y(1)=\beta\). More specifically, they propose a numerical scheme of collocation type using fourth order exponential splines. After giving the convergence theorem of order two for the numerical solution, they show two numerical examples to exhibit the less computational effort of their method than those of other methods of exponential type.
Reviewer: T.Mitsui

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
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