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Stable difference schemes with uneven mesh spacings

Author: Melvyn Ciment
Journal: Math. Comp. 25 (1971), 219-227
MSC: Primary 65N10
MathSciNet review: 0300470
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Abstract: We consider a finite-difference approximation to the Cauchy problem for a firstorder hyperbolic partial differential equation using different mesh spacings in different portions of the domain. By reformulating our problem as a difference approximation to an initial-boundary value problem, we are able to use the theory of H. O. Kreiss and S. Osher to analyze the $ {L_2}$ stability of our scheme.

References [Enhancements On Off] (What's this?)

  • [1] M. Ciment, Stable Difference Schemes With Uneven Mesh Spacings, A.E.C. Research and Development Report #NYO-1480-100, Ph.D. Thesis, New York University, New York, 1968.
  • [2] E. Isaacson & H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. MR 34 # 924. MR 0201039 (34:924)
  • [3] H. O. Kreiss, Difference Approximations for Initial-Boundary Value Problems for Hyperbolic Differential Equations, Proc. Adv. Sympos. Numerical Solutions of Partial Differential Equations (Madison, Wis., 1965), Wiley, New York, 1966, pp. 141-166. MR 35 #5156. MR 0214305 (35:5156)
  • [4] H. O. Kreiss, "Stability theory for difference approximations of mixed initial boundary value problems. I," Math. Comp., v. 22, 1968, pp. 703-714. MR 39 #2355. MR 0241010 (39:2355)
  • [5] P. D. Lax & B. Wendroff, "Difference schemes for hyperbolic equations with higher order accuracy," Comm. Pure Appl. Math., v. 17, 1964, 381-398. MR 30 #722. MR 0170484 (30:722)
  • [6] S. Osher, "Systems of difference equations with general homogeneous boundary conditions," Trans. Amer. Math. Soc., v. 137, 1969, pp. 177-201. MR 38 #6259. MR 0237982 (38:6259)
  • [7] R. D. Richtmyer & K. W. Morton, Difference Methods for Initial Value Problems, 2nd ed., Interscience Tracts in Pure and Appl. Math., no. 4, Interscience, New York, 1967. MR 36 #3515. MR 0220455 (36:3515)

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Keywords: Difference methods, stability, mixed initial-boundary value problems, mesh refinement
Article copyright: © Copyright 1971 American Mathematical Society

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