Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term

© 2015, Springer Science+Business Media New York. We formulate and analyze new methods for the solution of a partial integrodifferential equation with a positive-type memory term. These methods combine the finite element Galerkin (FEG) method for the spatial discretization with alternating direction...

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Main Authors: Morrakot Khebchareon, Amiya K. Pani, Graeme Fairweather
Format: Journal
Published: 2018
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/44376
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-443762018-04-25T07:49:21Z Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term Morrakot Khebchareon Amiya K. Pani Graeme Fairweather Agricultural and Biological Sciences © 2015, Springer Science+Business Media New York. We formulate and analyze new methods for the solution of a partial integrodifferential equation with a positive-type memory term. These methods combine the finite element Galerkin (FEG) method for the spatial discretization with alternating direction implicit (ADI) methods based on the Crank–Nicolson (CN) method and the second order backward differentiation formula for the time stepping. The ADI FEG methods are proved to be of optimal accuracy in time and in the $$L^2$$L2 norm in space. Furthermore, the analysis is extended to include an ADI CN FEG method with a graded mesh in time for problems with a nonsmooth kernel. Numerical results confirm the predicted convergence rates and also exhibit optimal spatial accuracy in the $$L^{\infty }$$L∞ norm. 2018-01-24T04:41:50Z 2018-01-24T04:41:50Z 2015-03-24 Journal 08857474 2-s2.0-84946483897 10.1007/s10915-015-0004-9 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84946483897&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/44376
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Agricultural and Biological Sciences
spellingShingle Agricultural and Biological Sciences
Morrakot Khebchareon
Amiya K. Pani
Graeme Fairweather
Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
description © 2015, Springer Science+Business Media New York. We formulate and analyze new methods for the solution of a partial integrodifferential equation with a positive-type memory term. These methods combine the finite element Galerkin (FEG) method for the spatial discretization with alternating direction implicit (ADI) methods based on the Crank–Nicolson (CN) method and the second order backward differentiation formula for the time stepping. The ADI FEG methods are proved to be of optimal accuracy in time and in the $$L^2$$L2 norm in space. Furthermore, the analysis is extended to include an ADI CN FEG method with a graded mesh in time for problems with a nonsmooth kernel. Numerical results confirm the predicted convergence rates and also exhibit optimal spatial accuracy in the $$L^{\infty }$$L∞ norm.
format Journal
author Morrakot Khebchareon
Amiya K. Pani
Graeme Fairweather
author_facet Morrakot Khebchareon
Amiya K. Pani
Graeme Fairweather
author_sort Morrakot Khebchareon
title Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
title_short Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
title_full Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
title_fullStr Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
title_full_unstemmed Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
title_sort alternating direction implicit galerkin methods for an evolution equation with a positive-type memory term
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84946483897&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/44376
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