On difference schemes for hyperbolic equations with discontinuous initial values
Author:
Mats Y. T. Apelkrans
Journal:
Math. Comp. 22 (1968), 525539
MSC:
Primary 65.67
MathSciNet review:
0233527
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References 
Similar Articles 
Additional Information
 [1]
Mats
Y. T. Apelkrans, On difference schemes for hyperbolic
equations with discontinuous initial values, Math. Comp. 22 (1968), 525–539. MR 0233527
(38 #1848), http://dx.doi.org/10.1090/S00255718196802335276
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P. Fedorenko, Application of highaccuracy difference schemes to
the numerical solution of hyperbolic equations, Ž.
Vyčisl. Mat. i Mat. Fiz. 2 (1962), 1122–1128
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0148231 (26 #5739)
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G. W. Hedström, ``The rate of convergence of some difference schemes.'' (To appear.)
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HeinzOtto
Kreiss, On difference approximations of the dissipative type for
hyperbolic differential equations, Comm. Pure Appl. Math.
17 (1964), 335–353. MR 0166937
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HeinzOtto
Kreiss and Einar
Lundqvist, On difference approximations with
wrong boundary values, Math. Comp. 22 (1968), 1–12. MR 0228193
(37 #3777), http://dx.doi.org/10.1090/S0025571819680228193X
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Peter
D. Lax, On the stability of difference approximations to solutions
of hyperbolic equations with variable coefficients, Comm. Pure Appl.
Math. 14 (1961), 497–520. MR 0145686
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D. Lax and L.
Nirenberg, On stability for difference schemes: A sharp form of
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G. Strang, ``Trigonometric polynomials and difference methods of maximum accuracy,'' J. Math, and Phys., v. 41, 1962, pp. 147154.
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Thomée, On maximumnorm stable difference operators,
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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 highaccuracy difference schemes to the numerical solution of hyperbolic equations,'' Ž. Vyčisl. Mat. i Mat. Fiz., v. 2, 1962, pp. 11221128. (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. 335353. 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. 112. 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. 497520. 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. 473492. MR 34 #6352. MR 0206534 (34:6352)
 [8]
 B. Parlett, ``Accuracy and dissipation in difference schemes,'' Comm. Pure Appl. Math., v. 19, 1966, pp. 111123. MR 33 #5141. MR 0196957 (33:5141)
 [9]
 J. Peetré & V. Thomée, ``On the rate of convergence for discrete initialvalue 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. 147154.
 [11]
 V. Thomée, ``On maximumnorm 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 InitialValue Problems, Interscience Tracts in Pure and Applied Mathematics, Interscience, New York, 1957. MR 20 #438. MR 0093918 (20:438)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196802335276
PII:
S 00255718(1968)02335276
Article copyright:
© Copyright 1968 American Mathematical Society
