메뉴 건너뛰기




Volumn 25, Issue 1-2, 2005, Pages 105-128

On high order strong stability preserving runge-kutta and multi step time discretizations

Author keywords

65L06; 65M20; high order accuracy; multi step methods; Runge Kutta methods; Strong stability preserving; time discretization

Indexed keywords

DISCRETE EVENT SIMULATION; NON NEWTONIAN FLOW; STABILITY;

EID: 85112679546     PISSN: 08857474     EISSN: 15737691     Source Type: Journal    
DOI: 10.1007/BF02728985     Document Type: Article
Times cited : (17)

References (37)
  • 1
    • 0004075585 scopus 로고
    • Fourth-order 2N-storage Runge-Kutta schemes
    • Carpenter, M., and Kennedy, C. (1994).Fourth-order 2N-storage Runge-Kutta schemes, NASA TM 109112, NASA Langley Research Center.
    • (1994) NASA TM 109112
    • Carpenter, M.1    Kennedy, C.2
  • 3
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework
    • Cockburn, B., and Shu, C.-W. (1989). TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework,Math. Comput. 52, 411–435. DOI: 10.2307/2008474
    • (1989) Math. Comput. , vol.52 , pp. 411-435
    • Cockburn, B.1    Shu, C.-W.2
  • 4
    • 28844447972 scopus 로고    scopus 로고
    • Stepsize Restrictions for the total variation diminishing property in general Runge-Kutta methods
    • Report MI 2002-21
    • Ferracina, L., and Spijker, M.N. (2002). Stepsize Restrictions for the total variation diminishing property in general Runge-Kutta methods.Num. Anal. Reports of Leiden University, Report MI 2002-21.
    • (2002) Num. Anal. Reports of Leiden University
    • Ferracina, L.1    Spijker, M.N.2
  • 5
    • 11244318599 scopus 로고    scopus 로고
    • An extension and analysis of the Shu-Osher representation of Runge-Kutta method
    • Ferracina, L., and Spijker, M.N. (2005). An extension and analysis of the Shu-Osher representation of Runge-Kutta method.Math. Comput. 74, 201–219. DOI: 10.1090/S0025-5718-04-01664-3
    • (2005) Math. Comput. , vol.74 , pp. 201-219
    • Ferracina, L.1    Spijker, M.N.2
  • 6
    • 0347900506 scopus 로고    scopus 로고
    • Strong stability preserving properties of Runge-Kutta time discretization methods for linear constant coefficient operators
    • Gottlieb, S., and Gottlieb, L.-J. (2003).Strong stability preserving properties of Runge-Kutta time discretization methods for linear constant coefficient operators, J. Sci. Compu. 18, 83–110. DOI: 10.1023/A:1020338228736
    • (2003) J. Sci. Compu. , vol.18 , pp. 83-110
    • Gottlieb, S.1    Gottlieb, L.-J.2
  • 7
    • 0032345207 scopus 로고    scopus 로고
    • Total variation diminishing Runge-Kutta schemes
    • Gottlieb, S., and Shu, C.-W. (1998). Total variation diminishing Runge-Kutta schemes,Math. Compu. 67, 73–85. DOI: 10.1090/S0025-5718-98-00913-2
    • (1998) Math. Compu. , vol.67 , pp. 73-85
    • Gottlieb, S.1    Shu, C.-W.2
  • 8
    • 0035273564 scopus 로고    scopus 로고
    • Strong stability preserving high-order time discretization methods
    • Gottlieb, S., Shu, C.-W., and Tadmor, E. (2001). Strong stability preserving high-order time discretization methods,SIAM Review 43, 89–112. DOI: 10.1137/S003614450036757X
    • (2001) SIAM Review , vol.43 , pp. 89-112
    • Gottlieb, S.1    Shu, C.-W.2    Tadmor, E.3
  • 9
    • 84966257131 scopus 로고
    • The CFL condition for spectral approximations to hyperbolic initial-boundary value problems
    • Gottlieb, D., and Tadmor, E. (1995). The CFL condition for spectral approximations to hyperbolic initial-boundary value problems,Math. Comput. 56, 565–588.
    • (1995) Math. Comput. , vol.56 , pp. 565-588
    • Gottlieb, D.1    Tadmor, E.2
  • 10
    • 85168423765 scopus 로고    scopus 로고
    • Strong stability preserving Runge-Kutta methods for fast downwind biased discretizations, to appear inJ
    • Gottlieb, S., and Ruuth, S.J. Strong stability preserving Runge-Kutta methods for fast downwind biased discretizations, to appear inJ. Sci. Comput.
    • Sci. Comput.
    • Gottlieb, S.1    Ruuth, S.J.2
  • 11
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • Harten, A. (1983).High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49, 357–393. DOI: 10.1016/0021-9991(83)90136-5
    • (1983) J. Comput. Phys. , vol.49 , pp. 357-393
    • Harten, A.1
  • 12
    • 3042714776 scopus 로고    scopus 로고
    • On strong stability preserving methods
    • Higueras, I. (2004) On strong stability preserving methods.J. Sci Comput. 21, 193–223. DOI: 10.1023/B:JOMP.0000030075.59237.61
    • (2004) J. Sci Comput. , vol.21 , pp. 193-223
    • Higueras, I.1
  • 14
    • 2342460322 scopus 로고    scopus 로고
    • Monotonicity-preserving linear multistep methods
    • Hundsdorfer, W., Ruuth, S.J., and Spiteri, R.J. (2003). Monotonicity-preserving linear multistep methods.SIAM J. Num. Anal. 41, 605–623. DOI: 10.1137/S0036142902406326
    • (2003) SIAM J. Num. Anal. , vol.41 , pp. 605-623
    • Hundsdorfer, W.1    Ruuth, S.J.2    Spiteri, R.J.3
  • 15
    • 0034316651 scopus 로고    scopus 로고
    • Low storage explicit Runge-Kutta schemes for the compressible navier-stokes equations
    • Kennedy, C., Carpenter, M., and Lewis, R. (2000). Low storage explicit Runge-Kutta schemes for the compressible navier-stokes equations,Appl. Nume. Math. 35, 177–219. DOI: 10.1016/S0168-9274(99)00141-5
    • (2000) Appl. Nume. Math. , vol.35 , pp. 177-219
    • Kennedy, C.1    Carpenter, M.2    Lewis, R.3
  • 16
    • 0001813542 scopus 로고
    • Absolute monotonicity of polynomials occurring in the numerical solution of initial value problems
    • Kraaijevanger, J.F.B.M. (1986).Absolute monotonicity of polynomials occurring in the numerical solution of initial value problems, Numerische Mathematik 48, 303–322. DOI: 10.1007/BF01389477
    • (1986) Numerische Mathematik , vol.48 , pp. 303-322
    • Kraaijevanger, J.F.B.M.1
  • 17
    • 0000625694 scopus 로고
    • Contractivity of Runge-Kutta methods
    • Kraaijevanger, J.F.B.M. (1991).Contractivity of Runge-Kutta methods, BIT 31, 482–528. DOI: 10.1007/BF01933264
    • (1991) BIT , vol.31 , pp. 482-528
    • Kraaijevanger, J.F.B.M.1
  • 19
    • 84966211896 scopus 로고
    • Contractivity preserving implicit linear multi step methods
    • Lenferink, H.W.J. (1991). Contractivity preserving implicit linear multi step methods,Math. Comput. 56, 177–199. DOI: 10.2307/2008536
    • (1991) Math. Comput. , vol.56 , pp. 177-199
    • Lenferink, H.W.J.1
  • 20
    • 0032014411 scopus 로고    scopus 로고
    • From semi-discrete to fully discrete: stability of Runge-Kutta schemes by the energy method
    • Levy, D. and Tadmor, E. (1998). From semi-discrete to fully discrete: stability of Runge-Kutta schemes by the energy method.SIAM Review,40, 40–73. DOI: 10.1137/S0036144597316255
    • (1998) SIAM Review , vol.40 , pp. 40-73
    • Levy, D.1    Tadmor, E.2
  • 21
    • 0000592595 scopus 로고
    • Weighted essentially non-oscillatory schemes
    • Liu, X-D., Osher, S., and Chan, T. (1994). Weighted essentially non-oscillatory schemesJ. Comput. Phys. 115 (1), 200. DOI: 10.1006/jcph.1994.1187
    • (1994) J. Comput. Phys. , vol.115 , Issue.1 , pp. 200
    • Liu, X.-D.1    Osher, S.2    Chan, T.3
  • 22
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • Nessyahu, H., and Tadmor, E. (1990). Non-oscillatory central differencing for hyperbolic conservation laws,J. Comp. Phys. 87, 408–463. DOI: 10.1016/0021-9991(90)90260-8
    • (1990) J. Comp. Phys. , vol.87 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 23
    • 0021513288 scopus 로고
    • High resolution schemes and the entropy condition
    • Osher, S., and Chakravarthy, S. (1984). High resolution schemes and the entropy condition.SIAM J. Num. Anal. 21, 955–984. DOI: 10.1137/0721060
    • (1984) SIAM J. Num. Anal. , vol.21 , pp. 955-984
    • Osher, S.1    Chakravarthy, S.2
  • 24
    • 84966232121 scopus 로고
    • On the convergence of difference approximations to scalar conservation laws
    • Osher, S., and Tadmor, E. (1988). On the convergence of difference approximations to scalar conservation laws.Math. Comp. 50, 19–51. DOI: 10.2307/2007913
    • (1988) Math. Comp. , vol.50 , pp. 19-51
    • Osher, S.1    Tadmor, E.2
  • 25
    • 0013150498 scopus 로고    scopus 로고
    • Two barriers on strong-stability-preserving time discretization methods
    • Ruuth, S.J., and Spiteri, R.J. (2002). Two barriers on strong-stability-preserving time discretization methods.J. Sci. Comp. 17, 211–220. DOI: 10.1023/A:1015156832269
    • (2002) J. Sci. Comp. , vol.17 , pp. 211-220
    • Ruuth, S.J.1    Spiteri, R.J.2
  • 26
    • 14844365146 scopus 로고    scopus 로고
    • Downwinding in high-order strong-stability-preserving Runge-Kutta methods
    • Ruuth, S.J., and Spiteri, R.J. (2004). Downwinding in high-order strong-stability-preserving Runge-Kutta methods.SIAM J. Numer. Anal. 42, 974–996. DOI: 10.1137/S0036142902419284
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 974-996
    • Ruuth, S.J.1    Spiteri, R.J.2
  • 28
    • 0000564951 scopus 로고
    • Total-variation-diminishing time discretizations
    • Shu, C.-W. (1988). Total-variation-diminishing time discretizations.SIAM J. Sci. Stat. Comput. 9, 1073–1084. DOI: 10.1137/0909073
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 1073-1084
    • Shu, C.-W.1
  • 29
    • 45449125925 scopus 로고    scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes
    • Shu, C.-W., and Osher, S. (1998). Efficient implementation of essentially non-oscillatory shock-capturing schemes.J. Comput. Phy. 77, 439–471. DOI: 10.1016/0021-9991(88)90177-5
    • (1998) J. Comput. Phy. , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 31
    • 0001118530 scopus 로고    scopus 로고
    • A new class of optimal high-order strong-stability-preserving time discretization methods
    • Spiteri, R.J., and Ruuth, S.J., (2002). A new class of optimal high-order strong-stability-preserving time discretization methods. SIAMJ. Numer. Anal. 40, 469–491. DOI: 10.1137/S0036142901389025
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 469-491
    • Spiteri, R.J.1    Ruuth, S.J.2
  • 32
    • 0037434586 scopus 로고    scopus 로고
    • Nonlinear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
    • Spiteri, R.J., and Ruuth, S.J. (2003). Nonlinear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods.J. Math. Comput. Simul. 62, 125–135. DOI: 10.1016/S0378-4754(02)00179-9
    • (2003) J. Math. Comput. Simul. , vol.62 , pp. 125-135
    • Spiteri, R.J.1    Ruuth, S.J.2
  • 33
    • 33748538768 scopus 로고
    • Accurate partial difference methods II: nonlinear problems
    • Strang, G. (1964). Accurate partial difference methods II: nonlinear problems.Numerische Mathematik 6, 37. DOI: 10.1007/BF01386051
    • (1964) Numerische Mathematik , vol.6 , pp. 37
    • Strang, G.1
  • 35
    • 0021513424 scopus 로고
    • High resolution schemes using flux limiters for hyperbolic conservation laws
    • Sweby, P.K. (1984) High resolution schemes using flux limiters for hyperbolic conservation laws.SIAM J. Num. Anal. 21, 995–1011. DOI: 10.1137/0721062
    • (1984) SIAM J. Num. Anal. , vol.21 , pp. 995-1011
    • Sweby, P.K.1
  • 36
    • 0002033981 scopus 로고
    • Approximate solutions of nonlinear conservation laws
    • Quarteroni A., (ed), Lectures Notes from CIME Course Cetraro, Italy, 1997 Lecture Notes Mathematics 1697, Springer US, Berlin
    • Tadmor, E. (1988). Approximate solutions of nonlinear conservation laws. In Quarteroni, A. (ed.), ”Advanced Numerical Approximation of Nonlinear Hyperbolic Equations,”Lectures Notes from CIME Course Cetraro, Italy, 1997 Lecture Notes in Mathematics 1697, Springer-Verlag, Berlin pp. 1–150.
    • (1988) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , pp. 1-150
    • Tadmor, E.1
  • 37
    • 0002255298 scopus 로고
    • Low-storage Runge-Kutta schemes
    • Williamson, J.H. (1980). Low-storage Runge-Kutta schemes.J. Comput. Phys. 35, 48–56. DOI: 10.1016/0021-9991(80)90033-9
    • (1980) J. Comput. Phys. , vol.35 , pp. 48-56
    • Williamson, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.