메뉴 건너뛰기




Volumn 53, Issue 8, 2007, Pages 1293-1305

An error analysis of the modified scaling and squaring method

Author keywords

function; Exponential integrators; Rounding error analysis; Scaling and squaring methods; Truncation error analysis

Indexed keywords

COMPUTATIONAL METHODS; ERROR ANALYSIS; FUNCTIONS; INTEGRATION; MATRIX ALGEBRA; MEASUREMENT ERRORS; ORDINARY DIFFERENTIAL EQUATIONS;

EID: 34248588219     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.04.032     Document Type: Article
Times cited : (15)

References (27)
  • 1
    • 10644287216 scopus 로고
    • The solution of ordinary differential equations with large time constants
    • Wiley, New York
    • Certaine J. The solution of ordinary differential equations with large time constants. Mathematical Methods for Digital Computers (1960), Wiley, New York 128-132
    • (1960) Mathematical Methods for Digital Computers , pp. 128-132
    • Certaine, J.1
  • 2
    • 0002279610 scopus 로고    scopus 로고
    • Exponential integrators for large systems of differential equations
    • Hochbruck M., Lubich C., and Selhofer H. Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput. 19 5 (1998) 1552-1574
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.5 , pp. 1552-1574
    • Hochbruck, M.1    Lubich, C.2    Selhofer, H.3
  • 3
    • 0001025210 scopus 로고    scopus 로고
    • A new class of time discretization schemes for the solution of nonlinear PDEs
    • Beylkin G., Keiser J.M., and Vozovoi L. A new class of time discretization 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
  • 4
    • 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 2 (2002) 430-455
    • (2002) J. Comput. Phys. , vol.176 , Issue.2 , pp. 430-455
    • Cox, S.M.1    Matthews, P.C.2
  • 5
    • 10844237437 scopus 로고    scopus 로고
    • Generalized integrating factor methods for stiff PDEs
    • Krogstad S. Generalized integrating factor methods for stiff PDEs. J. Comput. Phys. 203 1 (2005) 72-88
    • (2005) J. Comput. Phys. , vol.203 , Issue.1 , pp. 72-88
    • Krogstad, S.1
  • 6
    • 14844318087 scopus 로고    scopus 로고
    • Exponential Runge-Kutta methods for parabolic problems
    • Hochbruck M., and Ostermann A. Exponential Runge-Kutta methods for parabolic problems. Appl. Numer. Math. 53 (2005) 323-339
    • (2005) Appl. Numer. Math. , vol.53 , pp. 323-339
    • Hochbruck, M.1    Ostermann, A.2
  • 7
    • 34248571331 scopus 로고    scopus 로고
    • B. Minchev, W. Wright, A review of exponential integrators for first order semi-linear problem, Technical Report No. 2/2005, The Norwegian University of Science and Technology, 2005
  • 9
    • 0001332750 scopus 로고
    • Numerical computation of the matrix exponential with accuracy estimate
    • Ward R.C. Numerical computation of the matrix exponential with accuracy estimate. SIAM J. Numer. Anal. 14 4 (1977) 600-610
    • (1977) SIAM J. Numer. Anal. , vol.14 , Issue.4 , pp. 600-610
    • Ward, R.C.1
  • 10
    • 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 1 (2003) 3-49
    • (2003) SIAM Rev. , vol.45 , Issue.1 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 11
    • 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 1 (1992) 209-228
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.1 , pp. 209-228
    • Saad, Y.1
  • 12
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • Hochbruck M., and Lubich C. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34 5 (1997) 1911-1925
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.5 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 13
    • 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 1 (2003) 203-216
    • (2003) J. Comput. Appl. Math. , vol.161 , Issue.1 , pp. 203-216
    • Lu, Y.Y.1
  • 14
    • 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 4 (2005) 1214-1233
    • (2005) SIAM J. Sci. Comput. , vol.26 , Issue.4 , pp. 1214-1233
    • Kassam, A.-K.1    Trefethen, L.N.2
  • 15
    • 34248587844 scopus 로고    scopus 로고
    • H. Berland, B. Skaflestad, W. Wright, EXPINT - A MATLAB package for exponential integrators, Technical Report No. 4/2005, The Norwegian University of Science and Technology, 2005
  • 16
    • 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 4 (2005) 1179-1193
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , Issue.4 , pp. 1179-1193
    • Higham, N.J.1
  • 17
    • 0015039123 scopus 로고
    • An algorithm for the computation of the integral of the state transition matrix
    • Johnson J.C., and Phillips C.L. An algorithm for the computation of the integral of the state transition matrix. IEEE Trans. Automat. Control AC-16 (1971) 204-205
    • (1971) IEEE Trans. Automat. Control , vol.AC-16 , pp. 204-205
    • Johnson, J.C.1    Phillips, C.L.2
  • 18
    • 34248547118 scopus 로고    scopus 로고
    • G. Dahlquist, Stability and error bounds in the numerical integration of ordinary differential equations, Dissertation, 1958
  • 19
  • 25
    • 34248550519 scopus 로고    scopus 로고
    • N.J. Higham, The test matrix toolbox for MATLAB (Version 3.0), Numerical Analysis Report No. 276, Manchester Centre for Computational Mathematics, 1995
  • 26
    • 34248525987 scopus 로고    scopus 로고
    • FSF & GNU, GCC team GCC, GNU compiler collection. http://gcc.gnu.org, 2004
  • 27
    • 34248548586 scopus 로고    scopus 로고
    • M. Tommila, Apfloat, a C++ high performance arbitrary precision arithmetic package, Version 2.40. http://www.apfloat.org/, 2003


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.