• [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/S0025-5718-1968-0233527-6
• [2] R. P. Fedorenko, Application of high-accuracy difference schemes to the numerical solution of hyperbolic equations, Ž. Vyčisl. Mat. i Mat. Fiz. 2 (1962), 1122–1128 (Russian). MR 0148231 (26 #5739)
• [3] G. W. Hedström, ``The rate of convergence of some difference schemes.'' (To appear.)
• [4] Heinz-Otto Kreiss, On difference approximations of the dissipative type for hyperbolic differential equations, Comm. Pure Appl. Math. 17 (1964), 335–353. MR 0166937 (29 #4210)
• [5] Heinz-Otto 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/S0025-5718-1968-0228193-X
• [6] 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 (26 #3215)
• [7] P. D. Lax and L. Nirenberg, On stability for difference schemes: A sharp form of Gȧrding’s inequality, Comm. Pure Appl. Math. 19 (1966), 473–492. MR 0206534 (34 #6352)
• [8] Beresford Parlett, Accuracy and dissipation in difference schemes, Comm. Pure Appl. Math. 19 (1966), 111–123. MR 0196957 (33 #5141)
• [9] Jaak Peetre and Vidar Thomée, On the rate of convergence for discrete initial-value problems, Math. Scand. 21 (1967), 159–176 (1969). 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] Vidar Thomée, On maximum-norm stable difference operators, Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965), Academic Press, New York, 1966, pp. 125–151. MR 0210332 (35 #1225)
• [12] Robert D. Richtmyer, Difference methods for initial-value problems, Interscience tracts in pure and applied mathematics. Iract 4, Interscience Publishers, Inc., New. York, 1957. MR 0093918 (20 #438)

Bibliography

[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)