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 . We assume that the Cauchy data is of class BV, and we show that the sup norm of the error is bounded by at positive times.

**[1]**David Hoff,*A finite difference scheme for a system of two conservation laws with artificial viscosity*, Math. Comp.**33**(1979), no. 148, 1171–1193. MR**537964**, 10.1090/S0025-5718-1979-0537964-9**[2]**D. Hoff, "Invariant regions and finite difference schemes for systems of conservation laws." (To appear.)**[3]**Takaaki Nishida and Joel Smoller,*A class of convergent finite difference schemes for certain nonlinear parabolic systems*, Comm. Pure Appl. Math.**36**(1983), no. 6, 785–808. MR**720594**, 10.1002/cpa.3160360605**[4]**Joel Smoller,*Shock waves and reaction-diffusion equations*, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR**688146****[5]**Blake Temple,*Systems of conservation laws with invariant submanifolds*, Trans. Amer. Math. Soc.**280**(1983), no. 2, 781–795. MR**716850**, 10.1090/S0002-9947-1983-0716850-2**[6]**James Glimm,*Solutions in the large for nonlinear hyperbolic systems of equations*, Comm. Pure Appl. Math.**18**(1965), 697–715. MR**0194770****[7]**Ronald J. DiPerna,*Convergence of the viscosity method for isentropic gas dynamics*, Comm. Math. Phys.**91**(1983), no. 1, 1–30. MR**719807**

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0790643-8

Article copyright:
© Copyright 1985
American Mathematical Society