ISSN:
0749-159X
Keywords:
characteristic methods
;
Eulerian-Langrangian methods
;
numerical solution of first-order hyperbolic equations
;
Runge-Kutta methods
;
Mathematics and Statistics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We develop two Runge-Kutta characteristic methods for the solution of the initial-boundary value problems for first-order linear hyperbolic equations. One of the methods is based on a backtracking of the characteristics, while the other is based on forward tracking. The derived schemes naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary condition. They are fully mass conservative and can be viewed as higher-order time integration schemes improved over the ELLAM (Eulerian-Lagrangian localized adjoint method) method developed previously. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices. Extensive numerical results are presented to compare the performance of these methods with many well studied and widely used methods, including the Petrov-Galerkin methods, the streamline diffusion methods, the continuous and discontinuous Galerkin methods, the MUSCL, and the ENO schemes. The numerical experiments also verify the optimal-order convergence rates of the Runge-Kutta methods developed in this article. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 617-661, 1997
Additional Material:
27 Ill.
Type of Medium:
Electronic Resource
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