메뉴 건너뛰기




Volumn 59, Issue 3-4, 2009, Pages 468-486

Comparison of methods for evaluating functions of a matrix exponential

Author keywords

Exponential integrators; Exponential time differencing methods; Matrix exponential; Stiff differential equations

Indexed keywords

FUNCTIONS; PROBABILITY DENSITY FUNCTION;

EID: 58249084793     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2008.03.039     Document Type: Article
Times cited : (27)

References (32)
  • 1
    • 0347762801 scopus 로고    scopus 로고
    • A novel algorithm for the numerical integration of systems of ordinary differential equations arising in chemical problems
    • Aluffi-Pentini F., DeFonzo V., and Parisi V. A novel algorithm for the numerical integration of systems of ordinary differential equations arising in chemical problems. J. Math. Chem. 33 (2003) 1-15
    • (2003) J. Math. Chem. , vol.33 , pp. 1-15
    • Aluffi-Pentini, F.1    DeFonzo, V.2    Parisi, V.3
  • 2
    • 58249086636 scopus 로고    scopus 로고
    • H.A. Ashi, Numerical methods for stiff systems, PhD thesis, University of Nottingham, 2008, in preparation
    • H.A. Ashi, Numerical methods for stiff systems, PhD thesis, University of Nottingham, 2008, in preparation
  • 3
    • 33947657481 scopus 로고    scopus 로고
    • EXPINT - a MATLAB package for exponential integrators
    • Article 4, 17 pages
    • Berland H., Skaflestad B., and Wright W.M. EXPINT - a MATLAB package for exponential integrators. ACM Trans. Math. Software 33 1 (2007) 4 Article 4, 17 pages
    • (2007) ACM Trans. Math. Software , vol.33 , Issue.1 , pp. 4
    • Berland, H.1    Skaflestad, B.2    Wright, W.M.3
  • 4
    • 0001025210 scopus 로고    scopus 로고
    • A new class of time discretisation schemes for the solution of nonlinear PDEs
    • Beylkin G., Keiser J.M., and Vozovoi L. A new class of time discretisation schemes for the solution of nonlinear PDEs. J. Comput. Phys. 147 (1998) 362-387
    • (1998) J. Comput. Phys. , vol.147 , pp. 362-387
    • Beylkin, G.1    Keiser, J.M.2    Vozovoi, L.3
  • 6
    • 10644287216 scopus 로고
    • The solution of ordinary differential equations with large time constants
    • Ralston A., and Wilf H.S. (Eds), Wiley, New York
    • Certaine J. The solution of ordinary differential equations with large time constants. In: Ralston A., and Wilf H.S. (Eds). Mathematical Methods for Digital Computers (1960), Wiley, New York 128-132
    • (1960) Mathematical Methods for Digital Computers , pp. 128-132
    • Certaine, J.1
  • 7
    • 0036501083 scopus 로고    scopus 로고
    • Exponential time differencing for stiff systems
    • Cox S.M., and Matthews P.C. Exponential time differencing for stiff systems. J. Comput. Phys. 176 (2002) 430-455
    • (2002) J. Comput. Phys. , vol.176 , pp. 430-455
    • Cox, S.M.1    Matthews, P.C.2
  • 9
    • 27144549311 scopus 로고    scopus 로고
    • The scaling and squaring method for the matrix exponential revisited
    • Higham N.J. The scaling and squaring method for the matrix exponential revisited. SIAM J. Matrix Anal. Appl. 26 (2005) 1179-1193
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 1179-1193
    • Higham, N.J.1
  • 10
    • 33646264630 scopus 로고    scopus 로고
    • Explicit exponential Runge-Kutta methods for semilinear parabolic problems
    • Hochbruck M., and Ostermann A. Explicit exponential Runge-Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal. 43 (2005) 1069-1090
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 1069-1090
    • Hochbruck, M.1    Ostermann, A.2
  • 12
    • 58249092890 scopus 로고    scopus 로고
    • A.K. Kassam, High order timestepping for stiff semilinear partial differential equations, D. Phil. Thesis, Oxford University, 2004
    • A.K. Kassam, High order timestepping for stiff semilinear partial differential equations, D. Phil. Thesis, Oxford University, 2004
  • 13
    • 22544474620 scopus 로고    scopus 로고
    • Fourth-order time stepping for stiff PDEs
    • Kassam A.K., and Trefethen L.N. Fourth-order time stepping for stiff PDEs. SIAM J. Sci. Comput. 26 (2003) 1214-1233
    • (2003) SIAM J. Sci. Comput. , vol.26 , pp. 1214-1233
    • Kassam, A.K.1    Trefethen, L.N.2
  • 14
    • 34248588219 scopus 로고    scopus 로고
    • An error analysis of the modified scaling and squaring method
    • Koikari S. An error analysis of the modified scaling and squaring method. Comput. Math. Appl. 53 (2007) 1293-1305
    • (2007) Comput. Math. Appl. , vol.53 , pp. 1293-1305
    • Koikari, S.1
  • 15
    • 33845646844 scopus 로고    scopus 로고
    • An implementation of the exponential time differencing scheme to the magnetohydrodynamic equations in a spherical shell
    • Livermore P.W. An implementation of the exponential time differencing scheme to the magnetohydrodynamic equations in a spherical shell. J. Comput. Phys. 220 (2007) 824-838
    • (2007) J. Comput. Phys. , vol.220 , pp. 824-838
    • Livermore, P.W.1
  • 16
    • 0242458409 scopus 로고    scopus 로고
    • Computing a matrix function for exponential integrators
    • Lu Y.Y. Computing a matrix function for exponential integrators. J. Comput. Appl. Math. 161 (2003) 203-216
    • (2003) J. Comput. Appl. Math. , vol.161 , pp. 203-216
    • Lu, Y.Y.1
  • 18
    • 58249087825 scopus 로고    scopus 로고
    • B.V. Minchev, Computing analytic matrix functions for a class of exponential integrators, Reports in Informatics 278, University of Bergen, Bergen, Norway, 2004
    • B.V. Minchev, Computing analytic matrix functions for a class of exponential integrators, Reports in Informatics 278, University of Bergen, Bergen, Norway, 2004
  • 19
    • 0001143041 scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix
    • Moler C., and Van Loan C. Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev. 20 (1978) 801-836
    • (1978) SIAM Rev. , vol.20 , pp. 801-836
    • Moler, C.1    Van Loan, C.2
  • 20
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • Moler C., and Van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev. 45 (2003) 3-49
    • (2003) SIAM Rev. , vol.45 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 21
    • 0346196616 scopus 로고
    • An A-stable modification of the Adams-Bashforth methods
    • Dundee, 1969, Springer, Berlin
    • Nørsett S.P. An A-stable modification of the Adams-Bashforth methods. Conf. on Numerical Solution of Differential Equations. Dundee, 1969 (1969), Springer, Berlin 214-219
    • (1969) Conf. on Numerical Solution of Differential Equations , pp. 214-219
    • Nørsett, S.P.1
  • 22
    • 0002534227 scopus 로고
    • On the number of nonscalar multiplications necessary to evaluate polynomials
    • Paterson M.S., and Stockmeyer L.J. On the number of nonscalar multiplications necessary to evaluate polynomials. SIAM J. Comput. 2 (1973) 60-66
    • (1973) SIAM J. Comput. , vol.2 , pp. 60-66
    • Paterson, M.S.1    Stockmeyer, L.J.2
  • 23
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximations to the matrix exponential operator
    • Saad Y. Analysis of some Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 29 (1992) 209-228
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 209-228
    • Saad, Y.1
  • 24
    • 58249094076 scopus 로고    scopus 로고
    • T. Schmelzer, L.N. Trefethen, Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximations and contour integrals, Preprint, 2007
    • T. Schmelzer, L.N. Trefethen, Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximations and contour integrals, Preprint, 2007
  • 25
    • 0008711634 scopus 로고    scopus 로고
    • Review of FDTD time-stepping for efficient simulation of electric conductive media
    • Schuster C., Christ A., and Fichtner W. Review of FDTD time-stepping for efficient simulation of electric conductive media. Microwave Optical Technol. Lett. 25 (2000) 16-21
    • (2000) Microwave Optical Technol. Lett. , vol.25 , pp. 16-21
    • Schuster, C.1    Christ, A.2    Fichtner, W.3
  • 26
    • 0032010619 scopus 로고    scopus 로고
    • Expokit: A software package for computing matrix exponentials
    • Sidje R.B. Expokit: A software package for computing matrix exponentials. ACM Trans. Math. Softw. 24 (1998) 130-156
    • (1998) ACM Trans. Math. Softw. , vol.24 , pp. 130-156
    • Sidje, R.B.1
  • 27
    • 58249090454 scopus 로고    scopus 로고
    • The scaling and modified squaring method for matrix functions related to the exponential
    • Skaflestad B., and Wright W.M. The scaling and modified squaring method for matrix functions related to the exponential. Appl. Numer. Math. (2007)
    • (2007) Appl. Numer. Math.
    • Skaflestad, B.1    Wright, W.M.2
  • 28
    • 0022661834 scopus 로고
    • The exponential accuracy of Fourier and Chebyshev differencing methods
    • Tadmor E. The exponential accuracy of Fourier and Chebyshev differencing methods. SIAM J. Numer. Anal. 23 (1986) 1-10
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 1-10
    • Tadmor, E.1
  • 29
    • 0001942937 scopus 로고
    • Spectral methods in time for parabolic problems
    • Tal-Ezer H. Spectral methods in time for parabolic problems. SIAM J. Numer. Anal. 26 (1989) 1-11
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1-11
    • Tal-Ezer, H.1
  • 30
    • 32644441860 scopus 로고    scopus 로고
    • Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods
    • Tokman M. Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods. J. Comput. Phys. 213 (2006) 748-776
    • (2006) J. Comput. Phys. , vol.213 , pp. 748-776
    • Tokman, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.