메뉴 건너뛰기




Volumn 2, Issue 1, 2007, Pages 1-34

Implications of the choice of predictors for semi-implicit picard integral deferred correction methods

Author keywords

Deferred correction methods; Order reduction; semi implicit methods

Indexed keywords


EID: 37249056350     PISSN: 15593940     EISSN: 21575452     Source Type: Journal    
DOI: 10.2140/camcos.2007.2.1     Document Type: Article
Times cited : (30)

References (34)
  • 1
    • 0000496713 scopus 로고    scopus 로고
    • "On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations"
    • S. Abarbanel, D. Gottlieb, and M. H. Carpenter, "On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations", SIAM J. Sci. Comput. 17 (1996), 777-782
    • (1996) SIAM J. Sci. Comput , vol.17 , pp. 777-782
    • Abarbanel, S.1    Gottlieb, D.2    Carpenter, M.H.3
  • 2
    • 5144234666 scopus 로고    scopus 로고
    • "Implicit-explicit BDF methods for the Kuramoto-Silvashinsky equation"
    • G. Akrivis and Y.-S. Smyrlis, "Implicit-explicit BDF methods for the Kuramoto-Silvashinsky equation", Appl. Numer. Math. 51 (2004), 151-169
    • (2004) Appl. Numer. Math , vol.51 , pp. 151-169
    • Akrivis, G.1    Smyrlis, Y.-S.2
  • 3
    • 0032363607 scopus 로고    scopus 로고
    • "Implicit-explicit multistep finite element methods for nonlinear parabolic equations"
    • G. Akrivis, M. Crouzeix, and C. Makridakis, "Implicit-explicit multistep finite element methods for nonlinear parabolic equations", Math. Comp. 67 (1998), 457-477
    • (1998) Math. Comp , vol.67 , pp. 457-477
    • Akrivis, G.1    Crouzeix, M.2    Makridakis, C.3
  • 4
    • 0033439131 scopus 로고    scopus 로고
    • "Implicit-explicit multistep methods for quasilinear parabolic equations"
    • G. Akrivis,M. Crouzeix, and C. Makridakis, "Implicit-explicit multistep methods for quasilinear parabolic equations", Numer. Math. 82 (1999), 521-541
    • (1999) Numer. Math , vol.82 , pp. 521-541
    • Akrivis, G.1    Crouzeix, M.2    Makridakis, C.3
  • 5
    • 0036568582 scopus 로고    scopus 로고
    • "Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems"
    • B. Alonso-Mallo, I. and Cano, "Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems", Appl. Numer. Math. 41 (2002), 247-268
    • (2002) Appl. Numer. Math , vol.41 , pp. 247-268
    • Alonso-Mallo, B.1    Cano, I.2
  • 6
    • 0036627738 scopus 로고    scopus 로고
    • "Runge-Kutta methods without order reduction for intial boundary value problems"
    • I. Alonso-Mallo, "Runge-Kutta methods without order reduction for intial boundary value problems", Numer. Math. 91 (2002), 577-603
    • (2002) Numer. Math , vol.91 , pp. 577-603
    • Alonso-Mallo, I.1
  • 7
    • 0001737039 scopus 로고
    • "Implicit-explicit methods for time-dependent partial differential equations"
    • MR.96j:65076
    • U. M. Ascher, S. J. Ruuth, and B. T. R. Wetton, "Implicit-explicit methods for time-dependent partial differential equations", SIAM J. Numer. Anal. 32:3 (1995), 797-823. MR 96j:65076
    • (1995) SIAM J. Numer. Anal , vol.32 , Issue.3 , pp. 797-823
    • Ascher, U.M.1    Ruuth, S.J.2    Wetton, B.T.R.3
  • 8
    • 0031269714 scopus 로고    scopus 로고
    • "Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations"
    • U. M. Ascher, S. J. Ruuth, and R. J. Spiteri, "Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations", Appl. Numer. Math. 25 (1997), 151-167
    • (1997) Appl. Numer. Math , vol.25 , pp. 151-167
    • Ascher, U.M.1    Ruuth, S.J.2    Spiteri, R.J.3
  • 9
    • 48749141209 scopus 로고
    • "Adaptive mesh refinement for hyperbolic partial differential equations"
    • MR.85h:65211
    • M. J. Berger and J. Oliger, "Adaptive mesh refinement for hyperbolic partial differential equations", J. Comput. Phys. 53:3 (1984), 484-512. MR 85h:65211
    • (1984) J. Comput. Phys , vol.53 , Issue.3 , pp. 484-512
    • Berger, M.J.1    Oliger, J.2
  • 10
    • 0042657868 scopus 로고    scopus 로고
    • "Higher-order multi-implicit spectral deferred correction methods for problems of reacting flow"
    • A. Bourlioux, A. T. Layton, and M. L. Minion, "Higher-order multi-implicit spectral deferred correction methods for problems of reacting flow", J. Comput. Phys. 189 (2003), 351-376
    • (2003) J. Comput. Phys , vol.189 , pp. 351-376
    • Bourlioux, A.1    Layton, A.T.2    Minion, M.L.3
  • 11
    • 0036792332 scopus 로고    scopus 로고
    • "Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems"
    • MR.2003h:65091
    • M. P. Calvo and C. Palencia, "Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems", Math. Comp. 71:240 (2002), 1529-1543. MR 2003h:65091
    • (2002) Math. Comp , vol.71 , Issue.240 , pp. 1529-1543
    • Calvo, M.P.1    Palencia, C.2
  • 12
    • 0035370920 scopus 로고    scopus 로고
    • "Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations"
    • MR.2002e:65114
    • M. P. Calvo, J. de Frutos, and J. Novo, "Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations", Appl. Numer. Math. 37:4 (2001), 535-549. MR 2002e:65114
    • (2001) Appl. Numer. Math , vol.37 , Issue.4 , pp. 535-549
    • Calvo, M.P.1    de Frutos, J.2    Novo, J.3
  • 13
    • 0001186440 scopus 로고
    • "The theoretical accuracy of Runge-Kutta time discretizations for the initial-boundary value problem: a study of the boundary error"
    • MR.96h:65088
    • M. H. Carpenter, D. Gottlieb, S. Abarbanel, and W. S. Don, "The theoretical accuracy of Runge-Kutta time discretizations for the initial-boundary value problem: a study of the boundary error", SIAM J. Sci. Comput. 16:6 (1995), 1241-1252. MR 96h:65088
    • (1995) SIAM J. Sci. Comput , vol.16 , Issue.6 , pp. 1241-1252
    • Carpenter, M.H.1    Gottlieb, D.2    Abarbanel, S.3    Don, W.S.4
  • 14
    • 0042185232 scopus 로고    scopus 로고
    • "Spectral deferred correction methods for ordinary differential equations"
    • MR.2001e:65104
    • A. Dutt, L. Greengard, and V. Rokhlin, "Spectral deferred correction methods for ordinary differential equations", BIT 40:2 (2000), 241-266. MR 2001e:65104
    • (2000) BIT , vol.40 , Issue.2 , pp. 241-266
    • Dutt, A.1    Greengard, L.2    Rokhlin, V.3
  • 15
    • 85017510434 scopus 로고
    • On Padé approximations to the exponential function and A-stable methods for the numerical solution of initial value problems, Dept
    • Research Rpt. CSRR 2010, University of Waterloo
    • B. L. Ehle, On Padé approximations to the exponential function and A-stable methods for the numerical solution of initial value problems, Dept. Applied Analysis and Computer Sci., Research Rpt. CSRR 2010, University of Waterloo, 1969
    • (1969) Applied Analysis and Computer Sci
    • Ehle, B.L.1
  • 16
    • 0031275886 scopus 로고    scopus 로고
    • "On the stability of implicit-explicit linear multistep methods"
    • MR.98m:65126 . Special issue on time integration (Amsterdam, 1996)
    • J. Frank, W. Hundsdorfer, and J. G. Verwer, "On the stability of implicit-explicit linear multistep methods", Appl. Numer. Math. 25:2-3 (1997), 193-205. Special issue on time integration (Amsterdam, 1996). MR 98m:65126
    • (1997) Appl. Numer. Math , vol.25 , Issue.2-3 , pp. 193-205
    • Frank, J.1    Hundsdorfer, W.2    Verwer, J.G.3
  • 18
    • 0003589989 scopus 로고
    • II, Springer Series in Computational Mathematics 14, Springer, Berlin,. Stiff and differentialalgebraic problems. MR 92a:65016
    • E. Hairer and G. Wanner, Solving ordinary differential equations. II, Springer Series in Computational Mathematics 14, Springer, Berlin, 1991. Stiff and differentialalgebraic problems. MR 92a:65016
    • (1991) Solving ordinary differential equations
    • Hairer, E.1    Wanner, G.2
  • 19
    • 0036679952 scopus 로고    scopus 로고
    • "On the contractivity of implicit-explcit linear multistep methods"
    • K. J. in't Hout, "On the contractivity of implicit-explcit linear multistep methods", Appl. Numer. Math. 42 (2002), 201-212
    • (2002) Appl. Numer. Math , vol.42 , pp. 201-212
    • in't Hout, K.J.1
  • 20
    • 0037216570 scopus 로고    scopus 로고
    • "Additive Runge-Kutta schemes for convection-diffusion-reaction equations"
    • MR.2003m:65111
    • C. A. Kennedy and M. H. Carpenter, "Additive Runge-Kutta schemes for convection-diffusion-reaction equations", Appl. Numer. Math. 44:1-2 (2003), 139-181. MR 2003m:65111
    • (2003) Appl. Numer. Math , vol.44 , Issue.1-2 , pp. 139-181
    • Kennedy, C.A.1    Carpenter, M.H.2
  • 21
    • 1442282983 scopus 로고    scopus 로고
    • "Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics"
    • MR.2004k:76089
    • A. T. Layton and M. L. Minion, "Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics", J. Comput. Phys. 194:2 (2004), 697-715. MR 2004k:76089
    • (2004) J. Comput. Phys , vol.194 , Issue.2 , pp. 697-715
    • Layton, A.T.1    Minion, M.L.2
  • 22
    • 27144534869 scopus 로고    scopus 로고
    • "Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations"
    • MR.2006h:65087
    • A. T. Layton and M. L. Minion, "Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations", BIT 45:2 (2005), 341-373. MR 2006h:65087
    • (2005) BIT , vol.45 , Issue.2 , pp. 341-373
    • Layton, A.T.1    Minion, M.L.2
  • 23
    • 0034431558 scopus 로고    scopus 로고
    • "Central schemes for balance laws of relaxation type"
    • MR.2001j:65128
    • S. F. Liotta, V. Romano, and G. Russo, "Central schemes for balance laws of relaxation type", SIAM J. Numer. Anal. 38:4 (2000), 1337-1356. MR 2001j:65128
    • (2000) SIAM J. Numer. Anal , vol.38 , Issue.4 , pp. 1337-1356
    • Liotta, S.F.1    Romano, V.2    Russo, G.3
  • 24
    • 85128807957 scopus 로고    scopus 로고
    • "Semi-implicit spectral deferred correction methods for ordinary differential equations"
    • MR.2005f:65085
    • M. L. Minion, "Semi-implicit spectral deferred correction methods for ordinary differential equations", Commun. Math. Sci. 1:3 (2003), 471-500. MR 2005f:65085
    • (2003) Commun. Math. Sci , vol.1 , Issue.3 , pp. 471-500
    • Minion, M.L.1
  • 25
    • 1042275348 scopus 로고    scopus 로고
    • "Semi-implicit projection methods for incompressible flow based on spectral deferred corrections"
    • MR.MR2056924. Workshop on Innovative Time Integrators for PDEs
    • M. L. Minion, "Semi-implicit projection methods for incompressible flow based on spectral deferred corrections", Appl. Numer. Math. 48:3-4 (2004), 369-387. Workshop on Innovative Time Integrators for PDEs. MR MR2056924
    • (2004) Appl. Numer. Math , vol.48 , Issue.3-4 , pp. 369-387
    • Minion, M.L.1
  • 26
    • 0012148580 scopus 로고    scopus 로고
    • "Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations"
    • Nova Sci. Publ., Huntington, NY, 2001. MR 2005a:65065
    • L. Pareschi and G. Russo, "Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations", pp. 269-288 in Recent trends in numerical analysis, Adv. Theory Comput. Math. 3, Nova Sci. Publ., Huntington, NY, 2001. MR 2005a:65065
    • Recent trends in numerical analysis, Adv. Theory Comput. Math , vol.3 , pp. 269-288
    • Pareschi, L.1    Russo, G.2
  • 27
    • 28844475047 scopus 로고    scopus 로고
    • "Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation"
    • MR.MR2231946
    • L. Pareschi and G. Russo, "Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation", J. Sci. Comput. 25:1-2 (2005), 129-155. MR MR2231946
    • (2005) J. Sci. Comput , vol.25 , Issue.1-2 , pp. 129-155
    • Pareschi, L.1    Russo, G.2
  • 28
    • 0031215972 scopus 로고    scopus 로고
    • "The correct formulation of intermediate boundary conditions for Runge-Kutta time integration of initial-boundary value problems"
    • MR.98d:65100
    • D. Pathria, "The correct formulation of intermediate boundary conditions for Runge-Kutta time integration of initial-boundary value problems", SIAM J. Sci. Comput. 18:5 (1997), 1255-1266. MR 98d:65100
    • (1997) SIAM J. Sci. Comput , vol.18 , Issue.5 , pp. 1255-1266
    • Pathria, D.1
  • 29
    • 1042292758 scopus 로고    scopus 로고
    • "Avoiding order reduction of fractional step Runge-Kutta discretizations for linear time dependent coefficient parabolic problems"
    • MR.2005d:65153. Workshop on Innovative Time Integrators for PDEs
    • L. Portero, J. C. Jorge, and B. Bujanda, "Avoiding order reduction of fractional step Runge-Kutta discretizations for linear time dependent coefficient parabolic problems", Appl. Numer. Math. 48:3-4 (2004), 409-424. Workshop on Innovative Time Integrators for PDEs. MR 2005d:65153
    • (2004) Appl. Numer. Math , vol.48 , Issue.3-4 , pp. 409-424
    • Portero, L.1    Jorge, J.C.2    Bujanda, B.3
  • 30
    • 84968497765 scopus 로고
    • "On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations"
    • MR.48 #10125
    • A. Prothero and A. Robinson, "On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations", Math. Comp. 28 (1974), 145-162. MR 48 #10125
    • (1974) Math. Comp , vol.28 , pp. 145-162
    • Prothero, A.1    Robinson, A.2
  • 31
    • 0000391272 scopus 로고
    • "Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations"
    • MR.88f:65146
    • J. M. Sanz-Serna, J. G. Verwer, and W. H. Hundsdorfer, "Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations", Numer. Math. 50:4 (1987), 405-418. MR 88f:65146
    • (1987) Numer. Math , vol.50 , Issue.4 , pp. 405-418
    • Sanz-Serna, J.M.1    Verwer, J.G.2    Hundsdorfer, W.H.3
  • 32
    • 84959232904 scopus 로고    scopus 로고
    • "Semi-implicit Runge-Kutta schemes for the non-autonomous differential equations in reactive flow computations"
    • (New Orleans, 1996), Amer. Inst. Aeronautics and Astronautics, June
    • J. W. Shen and X. Zhong, "Semi-implicit Runge-Kutta schemes for the non-autonomous differential equations in reactive flow computations", in Proceedings of the 27th AIAA Fluid Dynamics Conference (New Orleans, 1996), Amer. Inst. Aeronautics and Astronautics, June 1996
    • (1996) Proceedings of the 27th AIAA Fluid Dynamics Conference
    • Shen, J.W.1    Zhong, X.2
  • 33
    • 0009419915 scopus 로고
    • "A note on unconditionally stable linear multistep methods"
    • MR.35 #6373
    • O. B. Widlund, "A note on unconditionally stable linear multistep methods", Nordisk Tidskr. Informations-Behandling 7 (1967), 65-70. MR 35 #6373
    • (1967) Nordisk Tidskr. Informations-Behandling , vol.7 , pp. 65-70
    • Widlund, O.B.1
  • 34
    • 0030269186 scopus 로고    scopus 로고
    • "Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows"
    • MR.97e:80019
    • X. Zhong, "Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows", J. Comput. Phys. 128:1 (1996), 19-31. MR 97e:80019
    • (1996) J. Comput. Phys , vol.128 , Issue.1 , pp. 19-31
    • Zhong, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.