A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of...

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Main Authors: Yong-Hong Fan, Lin-Lin Wang
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2018/8509860
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spelling doaj-69f90701fdc04c3abd40a5f30c8e4d972020-11-25T00:12:48ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/85098608509860A New Algorithm for Solving Terminal Value Problems of q-Difference EquationsYong-Hong Fan0Lin-Lin Wang1School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, ChinaSchool of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, ChinaWe propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.http://dx.doi.org/10.1155/2018/8509860
collection DOAJ
language English
format Article
sources DOAJ
author Yong-Hong Fan
Lin-Lin Wang
spellingShingle Yong-Hong Fan
Lin-Lin Wang
A New Algorithm for Solving Terminal Value Problems of q-Difference Equations
Discrete Dynamics in Nature and Society
author_facet Yong-Hong Fan
Lin-Lin Wang
author_sort Yong-Hong Fan
title A New Algorithm for Solving Terminal Value Problems of q-Difference Equations
title_short A New Algorithm for Solving Terminal Value Problems of q-Difference Equations
title_full A New Algorithm for Solving Terminal Value Problems of q-Difference Equations
title_fullStr A New Algorithm for Solving Terminal Value Problems of q-Difference Equations
title_full_unstemmed A New Algorithm for Solving Terminal Value Problems of q-Difference Equations
title_sort new algorithm for solving terminal value problems of q-difference equations
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2018-01-01
description We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.
url http://dx.doi.org/10.1155/2018/8509860
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AT linlinwang anewalgorithmforsolvingterminalvalueproblemsofqdifferenceequations
AT yonghongfan newalgorithmforsolvingterminalvalueproblemsofqdifferenceequations
AT linlinwang newalgorithmforsolvingterminalvalueproblemsofqdifferenceequations
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