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

MathSciNet review:
0233527

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**[1]**Mats Y. T. Apelkrans,*On difference schemes for hyperbolic equations with discontinuous initial values*, Math. Comp.**22**(1968), 525–539. MR**0233527**, 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****[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****[5]**Heinz-Otto Kreiss and Einar Lundqvist,*On difference approximations with wrong boundary values*, Math. Comp.**22**(1968), 1–12. MR**0228193**, 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****[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****[8]**Beresford Parlett,*Accuracy and dissipation in difference schemes*, Comm. Pure Appl. Math.**19**(1966), 111–123. MR**0196957****[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****[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****[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**

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

Article copyright:
© Copyright 1968
American Mathematical Society