The Optimal Convergence Rate for Monotone Finite Difference Schemes

SIAM Journal on Numerical Analysis Vol. 34, No. 6 (Dec., 1997), pp. 2306-2318

University of Alberta School of Business Research Paper No. 2013-1097

Posted: 2 Jul 2013

See all articles by Florin Sabac

Florin Sabac

University of Alberta - Department of Accounting, Operations & Information Systems

Date Written: June 1, 1996

Abstract

We are interested in the rate of convergence in L1 of the approximate solution of a conservation law generated by a monotone finite difference scheme. Kuznetsov has proved that this rate is 1/2 [USSR Comput. Math. Math. Phys., 16 (1976), pp. 105-119 and Topics Numer. Anal. III, in Proc. Roy. Irish Acad. Conf., Dublin, 1976, pp. 183-197], and recently Teng and Zhang have proved this estimate to be sharp for a linear flux [SIAM J. Numer. Anal., 34 (1997), pp. 959-978]. We prove, by constructing appropriate initial data for the Cauchy problem, that Kuznetsov's estimates are sharp for a nonlinear flux as well.

Suggested Citation

Sabac, Florin, The Optimal Convergence Rate for Monotone Finite Difference Schemes (June 1, 1996). SIAM Journal on Numerical Analysis Vol. 34, No. 6 (Dec., 1997), pp. 2306-2318, University of Alberta School of Business Research Paper No. 2013-1097, Available at SSRN: https://ssrn.com/abstract=2283394

Florin Sabac (Contact Author)

University of Alberta - Department of Accounting, Operations & Information Systems ( email )

Edmonton, Alberta T6G 2R6
Canada

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