An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations

An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations

In this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme...

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Main Author: Dunqian Cao
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/7056254
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spelling doaj-f05530b3d60d444196dbdcefd92561782020-11-25T03:44:06ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/70562547056254An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential EquationsDunqian Cao0School of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006, ChinaIn this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. The results show that the algorithm is high accurate and conditionally convergent, and an accuracy of 1/240h6 was achieved with smooth functions.http://dx.doi.org/10.1155/2020/7056254
collection DOAJ
language English
format Article
sources DOAJ
author Dunqian Cao
spellingShingle Dunqian Cao
An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations
Discrete Dynamics in Nature and Society
author_facet Dunqian Cao
author_sort Dunqian Cao
title An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations
title_short An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations
title_full An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations
title_fullStr An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations
title_full_unstemmed An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations
title_sort exponential spline difference scheme for solving a class of boundary value problems of second-order ordinary differential equations
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2020-01-01
description In this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. The results show that the algorithm is high accurate and conditionally convergent, and an accuracy of 1/240h6 was achieved with smooth functions.
url http://dx.doi.org/10.1155/2020/7056254
work_keys_str_mv AT dunqiancao anexponentialsplinedifferenceschemeforsolvingaclassofboundaryvalueproblemsofsecondorderordinarydifferentialequations
AT dunqiancao exponentialsplinedifferenceschemeforsolvingaclassofboundaryvalueproblemsofsecondorderordinarydifferentialequations
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