Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Note on a Classical Conservative Method for Scalar Hyperbolic Equations

  • Lee, Yong Hun (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Kim, Sang Dong (Department of Mathematics, Kyungpook National University)
  • Received : 2015.03.23
  • Accepted : 2015.07.28
  • Published : 2016.12.23
Download PDF
⟨ Previous Next ⟩

Abstract

We provide a combination of the forward Euler method and the trapezoidal quadrature rule leads to a two-step conservative numerical method which possesses TV-stable property together with consistency.

Keywords

Acknowledgement

Supported by : Kyungpook National University

References

  1. S. K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb., 47(1959), 271-306.
  2. A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49(1983), 357-393. https://doi.org/10.1016/0021-9991(83)90136-5
  3. R. J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics ETH Zurich, Birkhauser Verlag 1992.
  4. R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press 2002.
  5. B. van Leer, On the relation between the upwind-differencing schemes of Godunov, Engquist-Oscher and Roe, SIAM J. Sci. Stat. Comput., 5(1984), 1-20. https://doi.org/10.1137/0905001
  6. J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth and Brooks/Cole, 1989.
  7. J. W. Thomas, Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations, Texts in Applied Mathematics, 33, Springer-Verlag, 1999.