Stable difference schemes with uneven mesh spacings
Math. Comp. 25 (1971), 219-227
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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 stability of our scheme.
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.
Isaacson and Herbert
Bishop Keller, Analysis of numerical methods, John Wiley &
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Kreiss, Difference approximations for the initial-boundary value
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- E. Isaacson & H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. MR 34 # 924. MR 0201039 (34:924)
- 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)
- 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)
- 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)
- 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)
- 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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