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

Hoff, David; Smoller, Joel

doi:10.1090/S0025-5718-1985-0790643-8

Error bounds for finite-difference approximations for a class of nonlinear parabolic systems
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by David Hoff and Joel Smoller PDF

Math. Comp. 45 (1985), 35-49 Request permission

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 $O(\Delta x|\ln \Delta x|)$ at positive times.

References

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