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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Error bounds for finite-difference approximations for a class of nonlinear parabolic systems


Authors: David Hoff and Joel Smoller
Journal: Math. Comp. 45 (1985), 35-49
MSC: Primary 65M15; Secondary 35K99
MathSciNet review: 790643
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Abstract: In this paper we establish error bounds for a finite-difference approximation to solutions of certain parabolic systems of the form $ {v_t} + f{(v)_x} = \varepsilon {v_{xx}}$. We assume that the Cauchy data is of class BV, and we show that the sup norm of the error is bounded by $ O(\Delta x\vert\ln \Delta x\vert)$ at positive times.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1985-0790643-8
PII: S 0025-5718(1985)0790643-8
Article copyright: © Copyright 1985 American Mathematical Society