On difference schemes for hyperbolic equations with discontinuous initial values

Author:
Mats Y. T. Apelkrans

Journal:
Math. Comp. **22** (1968), 525-539

MSC:
Primary 65.67

DOI:
https://doi.org/10.1090/S0025-5718-1968-0233527-6

MathSciNet review:
0233527

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**[1]**M. Apelkrans,*On Difference Schemes for Hyperbolic Equations with Discontinuous Initial Values*, Report No. 5, Department of Computer Sciences, Uppsala, 1967. MR**0233527 (38:1848)****[2]**R. P. Fedorenko, ``The application of high-accuracy difference schemes to the numerical solution of hyperbolic equations,''*Ž. Vyčisl. Mat. i Mat. Fiz.*, v. 2, 1962, pp. 1122-1128. (Russian) MR**26**#5739. MR**0148231 (26:5739)****[3]**G. W. Hedström, ``The rate of convergence of some difference schemes.'' (To appear.)**[4]**H.-O. Kreiss, ``On difference approximations of the dissipative type for hyperbolic differential equations,''*Comm. Pure Appl. Math.*, v. 17, 1964, pp. 335-353. MR**29**#4210. MR**0166937 (29:4210)****[5]**H.-O. Kreiss & E. Lundqvist, ``On difference approximations with wrong boundary values,''*Math. Comp.*, v. 22, 1968, pp. 1-12. MR**0228193 (37:3777)****[6]**P. D. Lax, ``On the stability of difference approximations to solutions of hyperbolic equations with variable coefficients,''*Comm. Pure Appl. Math.*, v. 14, 1961, pp. 497-520. MR**26**#3215. MR**0145686 (26:3215)****[7]**P. D. Lax & L. Nirenberg, ``On stability for difference schemes: A sharp form of Gârding's Inequality,''*Comm. Pure Appl. Math.*, v. 19, 1966, pp. 473-492. MR**34**#6352. MR**0206534 (34:6352)****[8]**B. Parlett, ``Accuracy and dissipation in difference schemes,''*Comm. Pure Appl. Math.*, v. 19, 1966, pp. 111-123. MR**33**#5141. MR**0196957 (33:5141)****[9]**J. Peetré & V. Thomée, ``On the rate of convergence for discrete initial-value problems.'' (To appear.) MR**0255085 (40:8292)****[10]**G. Strang, ``Trigonometric polynomials and difference methods of maximum accuracy,''*J. Math, and Phys.*, v. 41, 1962, pp. 147-154.**[11]**V. Thomée, ``On maximum-norm stable difference operators'' in*Numerical Solution of Partial Differential Equations*, edited by, J. H. Bramble, Academic Press, New York, 1966. MR**0210332 (35:1225)****[12]**R. D. Richtmyer,*Difference Methods for Initial-Value Problems*, Interscience Tracts in Pure and Applied Mathematics, Interscience, New York, 1957. MR**20**#438. MR**0093918 (20:438)**

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0233527-6

Article copyright:
© Copyright 1968
American Mathematical Society