Remote Access Mathematics of Computation
Green Open Access

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
DOI: https://doi.org/10.1090/S0025-5718-1985-0790643-8
MathSciNet review: 790643
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] D. Hoff, "A finite difference scheme for a system of two conservation laws with artificial viscosity," Math. Comp., v. 33, 1979, pp. 1171-1193. MR 537964 (80k:65080)
  • [2] D. Hoff, "Invariant regions and finite difference schemes for systems of conservation laws." (To appear.)
  • [3] T. Nishida & J. Smoller, "A class of convergent finite difference schemes for certain nonlinear parabolic systems," Comm. Pure Appl. Math., v. 36, 1983, pp. 785-808. MR 720594 (85d:65050)
  • [4] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. MR 688146 (84d:35002)
  • [5] B. Temple, "Systems of conservation laws with invariant submanifolds," Trans. Amer. Math. Soc., v. 280, 1983, pp. 781-795. MR 716850 (84m:35080)
  • [6] J. Glimm, "Solutions in the large for nonlinear hyperbolic systems of equations," Comm. Pure Appl. Math., v. 18, 1965, pp. 697-715. MR 0194770 (33:2976)
  • [7] Ronald J. DiPerna, "Convergence of the viscosity method for isentropic gas dynamics," Comm. Math. Phys., v. 91, 1983, pp. 1-30. MR 719807 (85i:35118)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M15, 35K99

Retrieve articles in all journals with MSC: 65M15, 35K99


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1985-0790643-8
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society