A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations

A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations

We report a new numerical algorithm for solving one-dimensional linear parabolic partial differential equations (PDEs). The algorithm employs optimal quadratic spline collocation (QSC) for the space discretization and two-stage Gauss method for the time discretization. The new algorithm results in e...

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Main Authors: Jun Liu, Yan Wang
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2012/497365
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spelling doaj-f61e625012e643c08f28022538c516082020-11-25T00:49:07ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472012-01-01201210.1155/2012/497365497365A Numerical Method of High Accuracy for Linear Parabolic Partial Differential EquationsJun Liu0Yan Wang1College of Science, China University of Petroleum, Qingdao, Shandong 266580, ChinaCollege of Science, China University of Petroleum, Qingdao, Shandong 266580, ChinaWe report a new numerical algorithm for solving one-dimensional linear parabolic partial differential equations (PDEs). The algorithm employs optimal quadratic spline collocation (QSC) for the space discretization and two-stage Gauss method for the time discretization. The new algorithm results in errors of fourth order at the gridpoints of both the space partition and the time partition, and large time steps are allowed to save computational cost. The stability of the new algorithm is analyzed for a model problem. Numerical experiments are carried out to confirm the theoretical order of accuracy and demonstrate the effectiveness of the new algorithm.http://dx.doi.org/10.1155/2012/497365
collection DOAJ
language English
format Article
sources DOAJ
author Jun Liu
Yan Wang
spellingShingle Jun Liu
Yan Wang
A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations
Mathematical Problems in Engineering
author_facet Jun Liu
Yan Wang
author_sort Jun Liu
title A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations
title_short A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations
title_full A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations
title_fullStr A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations
title_full_unstemmed A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations
title_sort numerical method of high accuracy for linear parabolic partial differential equations
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2012-01-01
description We report a new numerical algorithm for solving one-dimensional linear parabolic partial differential equations (PDEs). The algorithm employs optimal quadratic spline collocation (QSC) for the space discretization and two-stage Gauss method for the time discretization. The new algorithm results in errors of fourth order at the gridpoints of both the space partition and the time partition, and large time steps are allowed to save computational cost. The stability of the new algorithm is analyzed for a model problem. Numerical experiments are carried out to confirm the theoretical order of accuracy and demonstrate the effectiveness of the new algorithm.
url http://dx.doi.org/10.1155/2012/497365
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AT yanwang anumericalmethodofhighaccuracyforlinearparabolicpartialdifferentialequations
AT junliu numericalmethodofhighaccuracyforlinearparabolicpartialdifferentialequations
AT yanwang numericalmethodofhighaccuracyforlinearparabolicpartialdifferentialequations
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