Large time asymptotic and numerical solution of a nonlinear diffusion model with memory
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Authors
Jangveladze, Temur
Neta, Beny
Kiguradze, Zurab
Subjects
System of nonlinear integro-differential equations
Large time behavior
Finite difference scheme
Large time behavior
Finite difference scheme
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Date of Issue
2010
Date
Publisher
Elsevier
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Abstract
Large time behavior of solutions and finite difference approximation of a nonlinear system of integro-differential equations associated with the penetration of a magnetic field into a substance is studied. Two initial-boundary value problems are investigated: the first with homogeneous conditions on whole boundary and the second with nonhomogeneous boundary data on one side of lateral boundary. The rates of convergence are also given. Mathematical results presented show that there is a difference between stabilization rates of solutions with homogeneous and nonhomogeneous boundary conditions. The convergence of the corresponding finite difference scheme is also proved. The decay of the numerical solution is compared with the analytical results.
Type
Article
Description
Computers and Mathematics with Applications, 59, (2010), 254–273
The article of record as published may be located at http://dx.doi.org/10.1016/j.camwa.2009.07.052
The article of record as published may be located at http://dx.doi.org/10.1016/j.camwa.2009.07.052
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Department
Applied Mathematics
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.