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Runge–Kutta characteristic methods for first‐order linear hyperbolic equations
Author(s) -
Wang Hong,
AlLawatia Mohamed,
Telyakovskiy Aleksey S.
Publication year - 1997
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199711)13:6<617::aid-num3>3.0.co;2-u
Subject(s) - mathematics , runge–kutta methods , discontinuous galerkin method , boundary value problem , partial differential equation , hyperbolic partial differential equation , convergence (economics) , numerical analysis , galerkin method , mathematical analysis , finite element method , physics , economics , thermodynamics , economic growth
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