On the optimally convergent splines difference scheme for one-dimensional reaction-diffusion problem
type: Item
instance of: scholarly article
title: On the optimally convergent splines difference scheme for one-dimensional reaction-diffusion problem
zbMATH Open document ID: 0808.65082
DOI: 10.1016/0307-904X(94)90308-5
published in: Applied Mathematical Modelling
publication date: 1995-03-22T00:00:00Z
review text: The author proposes a second-order optimally accurate difference scheme for selfadjoint perturbation problems of the following form: \(\varepsilon u'' + p(x)u = f(x)\), \(x \in [0,1]\), \(u(0) = \alpha_ 0\), \(u(1) = \alpha_ 1\), where \(p,f \in C^ 2[0,1]\), \(0 < \varepsilon \ll 1\), \(p(x) > \beta > 0\), \(x\in [0,1]\). The second section describes the difference discretization for the selfadjoint perturbation problem based on the exponential splines. The main idea is to use the continuous condition of the first derivative of exponential splines at midpoints. Section 3 proves that the scheme possesses second-order optimal convergence. The results are supported with the numerical experiments from Section 4.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 679971
zbMATH Keywords: difference scheme
zbMATH Keywords: selfadjoint perturbation problems
zbMATH Keywords: exponential splines
zbMATH Keywords: second-order optimal convergence
zbMATH Keywords: numerical experiments
author: Mirjana Stojanović
reviewed by: Dana Petcu
MaRDI profile type: Publication
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full work available at URL: 0307-904x(94)90308-5
OpenAlex ID: W2046261590
description: scientific article; zbMATH DE number 679971