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

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Title Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
 
Creator KHEBCHAREON, M
PANI, AK
FAIRWEATHER, G
 
Subject NUMERICAL-SOLUTION
LAPLACE TRANSFORMATION
DISCRETIZATION
QUADRATURE
Partial integrodifferential equation
Positive-type memory term
Finite element Galerkin method
Alternating direction implicit methods
Optimal error estimates
Smooth and nonsmooth kernels
 
Description 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 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 norm.
 
Publisher SPRINGER/PLENUM PUBLISHERS
 
Date 2016-01-14T12:10:49Z
2016-01-14T12:10:49Z
2015
 
Type Article
 
Identifier JOURNAL OF SCIENTIFIC COMPUTING, 65(3)1166-1188
0885-7474
1573-7691
http://dx.doi.org/10.1007/s10915-015-0004-9
http://dspace.library.iitb.ac.in/jspui/handle/100/17463
 
Language en