Intermediate boundary conditions for time-split methods applied to hyperbolic partial differential equations

Author:
Randall J. LeVeque

Journal:
Math. Comp. **47** (1986), 37-54

MSC:
Primary 65M05; Secondary 76B15

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842122-8

MathSciNet review:
842122

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Abstract: When time-split or fractional step methods are used to solve partial differential equations numerically, nonphysical intermediate solutions are introduced for which boundary data must often be specified. Here the appropriate boundary conditions are derived for splittings of hyperbolic problems into subproblems with disparate wave speeds. Numerical experiments are performed for the one-dimensional shallow water equations, a quasilinear system with inflow-outflow boundaries. Stability of the initial-boundary value problem is demonstrated for boundary conditions of the type derived here.

**[1]**M. Goldberg & E. Tadmor, "Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I,"*Math. Comp.*, v. 32, 1978, pp. 1097-1107. MR**501998 (80a:65196)****[2]**M. Goldberg & E. Tadmor, "Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II,"*Math. Comp.*, v. 36, 1981, pp. 603-626. MR**606519 (83f:65142)****[3]**B. Gustafsson, H.-O. Kreiss & A. Sundström, "Stability theory of difference approximations for mixed initial boundary value problems. II,"*Math. Comp.*, v. 26, 1972, pp. 649-685. MR**0341888 (49:6634)****[4]**R. J. LeVeque,*Time-Split Methods for Partial Differential Equations*. Ph.D. Thesis, Stanford Computer Science Department report STAN-CS-82-904, 1982.**[5]**R. J. LeVeque & J. Oliger, "Numerical methods based on additive splittings for hyperbolic partial differential equations,"*Math. Comp.*, v. 40, 1983, pp. 469-497. MR**689466 (84c:65116)****[6]**R. D. Richtmyer & K. W. Morton,*Difference Methods for Initial-Value Problems*, Interscience Tracts in Pure and Appl. Math., No. 4, Wiley, New York, 1967. MR**0220455 (36:3515)****[7]**G. Strang, "On the construction and comparison of difference schemes,"*SIAM J. Numer Anal.*, v. 5, 1968, pp. 506-517. MR**0235754 (38:4057)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842122-8

Keywords:
Time-split method,
fractional step method,
boundary conditons for finite-difference approximations

Article copyright:
© Copyright 1986
American Mathematical Society