Runge-Kutta Characteristic Methods for First-Order Linear Hyperbolic Equations

Hong Wang*, Mohamed Al-Lawatia, Aleksey S. Telyakovskiy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)617-661
Number of pages45
JournalNumerical Methods for Partial Differential Equations
Issue number6
Publication statusPublished - Nov 1997
Externally publishedYes


  • Characteristic methods
  • Eulerian-Lagrangian methods
  • Numerical solution of first-order hyperbolic equations
  • Rung-Kutta methods

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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