1 |
D. Estep, A modified equation for dispersive difference schemes, Appl. Number. Math., 17(1995), 299-309.
DOI
|
2 |
S. K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb., 47(1959), 271-306.
|
3 |
D. F. Griffiths and J. M. Sanz-Serna, On the scope of the method of modified equations, SIAM J. Sci. Statist. Comput., 7(1986), 994-1008.
DOI
|
4 |
A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49(1983), 357-393.
DOI
|
5 |
C. Hirsch, Numerical computation of internal and external flows, 2, Wiley, 1990.
|
6 |
N. Jiang, On the convergence of fully-discrete high-resolution schemes with van Leer's flux limiter for conservation laws, Methods Appl. Anal., 16(3)(2009), 403-422.
DOI
|
7 |
S. Konyagin, B. Popov and O. Trifonov, On convergence of minmod-type schemes, SAIM J. Numer. Anal., 42(5)(2005), 1978-1997.
DOI
|
8 |
B. Popov, and O. Trifonov, Order of convergence of second order schemes based on the minmod limiter, Math. Comp., 75(2006), 1735-1753.
DOI
|
9 |
G. Hedstrom, Models of difference schemes for ut + ux = 0 by partial differential equations, Math. Comp., 29(1975), 969-977.
DOI
|
10 |
P. K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SAIM J. Numer. Anal., 21(1984), 995-1011.
DOI
|
11 |
P. L. Roe, Some contributions to the modelling of discontinuous flows, Large-scale computations in fluid mechanics, Part 2 (La Jolla, Calif., 1983), 163-193, Lectures in Appl. Math. 22-2, Amer. Math. Soc., Providence, RI, 1985.
|
12 |
C. B. Laney, Computational gasdynamics, Cambridge University Press, Cambridge, 1998.
|
13 |
Y. H. Lee and S. D. Kim, Note on a classical conservative method for scalar hyperbolic equations, Kyungpook Math. J., 56(2016), 1179-1189.
DOI
|
14 |
B. van Leer, Towards the ultimate conservative difference scheme V. A second order sequel to Godunov's method, J. Comput. Phys., 32(1979), 101-136.
DOI
|
15 |
C.-W. Shu, TVB uniformly high-order schemes for conservation laws, Math. Comp., 49(1987), 105-121.
DOI
|
16 |
B. van Leer, On the relation between the upwind-differencing schemes of Godunov, Engquist-Oscher and Roe, SIAM J. Sci. Statist. Comput., 5(1984), 1-20.
DOI
|
17 |
R. J. LeVeque, Numerical methods for conservation laws, Lectures in Mathematics ETH Zurich, Birkhauser Verlag, 1992.
|
18 |
R. J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002.
|
19 |
R. F. Warming and B. J. Hyett, The modified equation approach to the stability and accuracy analysis of finite-difference methods, J. Comput. Phys., 14(1974), 159-179.
DOI
|
20 |
B. van Leer, Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme, J. Comput. Phys., 23(1997), 361-370.
|