메뉴 건너뛰기




Volumn 33, Issue 1, 2007, Pages

EXPINT - A MATLAB package for exponential integrators

Author keywords

Exponential integrators for semilinear problems; MATLAB; Multistep methods; Runge Kutta methods; Scaling and squaring technique

Indexed keywords

COMPUTER SOFTWARE; PROBLEM SOLVING; RUNGE KUTTA METHODS; SCALABILITY; SOFTWARE ENGINEERING;

EID: 33947657481     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1206040.1206044     Document Type: Article
Times cited : (113)

References (30)
  • 1
    • 33747166098 scopus 로고    scopus 로고
    • B-series and order conditions for exponential integrators
    • BERLAND, H., OWREN, B., AND SKAFLESTAD, B. 2005. B-series and order conditions for exponential integrators. SIAM J. Numer. Anal. 43, 4, 1715-1727.
    • (2005) SIAM J. Numer. Anal , vol.43 , Issue.4 , pp. 1715-1727
    • BERLAND, H.1    OWREN, B.2    SKAFLESTAD, B.3
  • 2
    • 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. 1998. A new class of time discretization schemes for the solution of nonlinear PDEs. J. Comp. Phys. 147, 362-387.
    • (1998) J. Comp. Phys , vol.147 , pp. 362-387
    • BEYLKIN, G.1    KEISER, J.M.2    VOZOVOI, L.3
  • 3
    • 0001356367 scopus 로고
    • Nonlinear stability for a general class of differential equation methods
    • BURRAGE, K. AND BUTCHER, J. C. 1980. Nonlinear stability for a general class of differential equation methods. BIT 20, 185-203.
    • (1980) BIT 20 , pp. 185-203
    • BURRAGE, K.1    BUTCHER, J.C.2
  • 5
    • 29144478020 scopus 로고    scopus 로고
    • A class of multistep exponential integrators for semilinear problems
    • CALVO, M. AND PALENCIA, C. 2006. A class of multistep exponential integrators for semilinear problems. Numer. Math. 102, 367-381.
    • (2006) Numer. Math , vol.102 , pp. 367-381
    • CALVO, M.1    PALENCIA, C.2
  • 7
    • 10644287216 scopus 로고
    • The solution of ordinary differential equations with large time constants
    • Wiley, New York, NY
    • CERTAINE, J. 1960. The solution of ordinary differential equations with large time constants. In Mathematical Methods for Digital Computers. Wiley, New York, NY, 128-132.
    • (1960) Mathematical Methods for Digital Computers , pp. 128-132
    • CERTAINE, J.1
  • 8
    • 0036501083 scopus 로고    scopus 로고
    • Exponential time differencing for stiff systems
    • COX, S. M. AND MATTHEWS, P. C. 2002. Exponential time differencing for stiff systems. J. Comput. Phys. 176, 2, 430-455.
    • (2002) J. Comput. Phys , vol.176 , Issue.2 , pp. 430-455
    • COX, S.M.1    MATTHEWS, P.C.2
  • 9
    • 2442552735 scopus 로고
    • Generalized Runge-Kutta processes for stiff initial-value problems
    • EHLE, B. L. AND LAWSON, J. D. 1975. Generalized Runge-Kutta processes for stiff initial-value problems. J. Inst. Math. Appl. 16, 11-21.
    • (1975) J. Inst. Math. Appl , vol.16 , pp. 11-21
    • EHLE, B.L.1    LAWSON, J.D.2
  • 10
    • 0346099850 scopus 로고
    • Verallgemeinerte Runge-Kutta Verfahren zur Lösung steifer Differentialgleichungssysteme
    • Numerical Treatment of Differential Equations, Springer, Berlin, Germany
    • FRIEDLI, A. 1978. Verallgemeinerte Runge-Kutta Verfahren zur Lösung steifer Differentialgleichungssysteme. In Numerical Treatment of Differential Equations. Lecture Notes in Mathematics, vol. 631. Springer, Berlin, Germany, 35-50.
    • (1978) Lecture Notes in Mathematics , vol.631 , pp. 35-50
    • FRIEDLI, A.1
  • 11
    • 0024779854 scopus 로고
    • A method for the exponential propagation of large stiff nonlinear differential equations
    • FRIESNER, R. A., TUCKERMAN, L. S., DORNBLASER, B. C., AND RUSSO, T. V. 1989. A method for the exponential propagation of large stiff nonlinear differential equations. J. Sci. Comput. 4, 4, 327-354.
    • (1989) J. Sci. Comput , vol.4 , Issue.4 , pp. 327-354
    • FRIESNER, R.A.1    TUCKERMAN, L.S.2    DORNBLASER, B.C.3    RUSSO, T.V.4
  • 12
    • 0000269389 scopus 로고
    • Efficient solution of parabolic equations by Krylov approximation methods
    • GALLOPOULOS, E. AND SAAD, Y 1992. Efficient solution of parabolic equations by Krylov approximation methods. SIAM J. Sci. Statist. Comput. 13, 1236-1264.
    • (1992) SIAM J. Sci. Statist. Comput , vol.13 , pp. 1236-1264
    • GALLOPOULOS, E.1    SAAD, Y.2
  • 13
    • 0036457301 scopus 로고    scopus 로고
    • 2nd ed. Society for Industrial and Applied Mathematics SIAM, Philadelphia, PA
    • HIGHAM, N. J. 2002. Accuracy and stability of numerical algorithms, 2nd ed. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
    • (2002) Accuracy and stability of numerical algorithms
    • HIGHAM, N.J.1
  • 14
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • HOCHBRUCK, M. AND LUBICH, C. 1997. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34, 5, 1911-1925.
    • (1997) SIAM J. Numer. Anal , vol.34 , Issue.5 , pp. 1911-1925
    • HOCHBRUCK, M.1    LUBICH, C.2
  • 15
    • 0002279610 scopus 로고    scopus 로고
    • Exponential integrators for large systems of differential equations
    • HOCHBRUCK, M., LUBICH, C., AND SELHOFER, H. 1998. Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput. 19, 5, 1552-1574.
    • (1998) SIAM J. Sci. Comput , vol.19 , Issue.5 , pp. 1552-1574
    • HOCHBRUCK, M.1    LUBICH, C.2    SELHOFER, H.3
  • 16
    • 33646264630 scopus 로고    scopus 로고
    • Explicit exponential Runge-Kutta methods for semi-linear parabolic problems
    • HOCHBRUCK, M. AND OSTERMANN, A. 2005. Explicit exponential Runge-Kutta methods for semi-linear parabolic problems. SIAM J. Numer. Anal. 43, 3, 1069-1090.
    • (2005) SIAM J. Numer. Anal , vol.43 , Issue.3 , pp. 1069-1090
    • HOCHBRUCK, M.1    OSTERMANN, A.2
  • 17
    • 85140870992 scopus 로고    scopus 로고
    • KASSAM, A.-K. AND TREFETHEN, L. N. 2005. Fourth-order time-stepping for stiff PDEs. SIAM J. Sci. Comput. 26, 4, 1214-1233 (electronic).
    • KASSAM, A.-K. AND TREFETHEN, L. N. 2005. Fourth-order time-stepping for stiff PDEs. SIAM J. Sci. Comput. 26, 4, 1214-1233 (electronic).
  • 18
    • 10844237437 scopus 로고    scopus 로고
    • Generalized integrating factor methods for stiff PDEs
    • KROGSTAD, S. 2005. Generalized integrating factor methods for stiff PDEs. J. Comp. Phys. 203, 1, 72-88.
    • (2005) J. Comp. Phys , vol.203 , Issue.1 , pp. 72-88
    • KROGSTAD, S.1
  • 19
    • 0001202958 scopus 로고
    • Generalized Runge-Kutta processes for stable systems with large Lipschitz constants
    • LAWSON, J. D. 1967. Generalized Runge-Kutta processes for stable systems with large Lipschitz constants. SIAM J. Numer. Anal. 4, 372-380.
    • (1967) SIAM J. Numer. Anal , vol.4 , pp. 372-380
    • LAWSON, J.D.1
  • 20
    • 0242458409 scopus 로고    scopus 로고
    • Computing a matrix function for exponential integrators
    • LU, Y. Y. 2003. Computing a matrix function for exponential integrators. J. Comput. Appl. Math 161, 1, 203-216.
    • (2003) J. Comput. Appl. Math , vol.161 , Issue.1 , pp. 203-216
    • LU, Y.Y.1
  • 21
    • 33747159634 scopus 로고    scopus 로고
    • A review of exponential integrators for semilinear problems
    • Tech. rep. 2/05. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway. Available online at
    • MINCHEV, B. AND WRIGHT, W. M. 2005. A review of exponential integrators for semilinear problems. Tech. rep. 2/05. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway. Available online at http://www.math.ntnu.no/preprint/.
    • (2005)
    • MINCHEV, B.1    WRIGHT, W.M.2
  • 22
    • 0037354371 scopus 로고    scopus 로고
    • MOLER, C. B. AND VAN LOAN, C. F. 2003. Nineteen dubious ways to compute the exponential of a matrix, twenty five years later. SIAM Review 45, 1, 3-49.
    • MOLER, C. B. AND VAN LOAN, C. F. 2003. Nineteen dubious ways to compute the exponential of a matrix, twenty five years later. SIAM Review 45, 1, 3-49.
  • 23
    • 0032739660 scopus 로고    scopus 로고
    • MUNTHE-KAAS, H. 1999. High order Runge-Kutta methods on manifolds. In Proceedings of the NSF/CBMS Regional Conference on Numerical Analysis of Hamiltonian Differential Equations (Golden, CO, 1997). Appl. Numer. Math. 29, 1, 115-127.
    • MUNTHE-KAAS, H. 1999. High order Runge-Kutta methods on manifolds. In Proceedings of the NSF/CBMS Regional Conference on Numerical Analysis of Hamiltonian Differential Equations (Golden, CO, 1997). Appl. Numer. Math. 29, 1, 115-127.
  • 25
    • 33745319450 scopus 로고    scopus 로고
    • A class of explicit exponential general linear methods
    • OSTEHMANN, A., THALHAMMER, M., AND WRIGHT, W. M. 2006. A class of explicit exponential general linear methods. BIT 46, 409-431.
    • (2006) BIT 46 , pp. 409-431
    • OSTEHMANN, A.1    THALHAMMER, M.2    WRIGHT, W.M.3
  • 26
    • 84966222159 scopus 로고
    • Krylov subspace methods for solving large unsymmetric linear systems
    • SAAD, Y. 1981. Krylov subspace methods for solving large unsymmetric linear systems. Math. Comp. 37, 105-126.
    • (1981) Math. Comp , vol.37 , pp. 105-126
    • SAAD, Y.1
  • 27
    • 33947709011 scopus 로고    scopus 로고
    • The scaling and modified squaring method for functions related to the exponential. appl
    • Submitted
    • SKAFLESTAD, B. AND WRIGHT, W. M. 2006. The scaling and modified squaring method for functions related to the exponential. appl. Numer. Math. Submitted.
    • (2006) Numer. Math
    • SKAFLESTAD, B.1    WRIGHT, W.M.2
  • 28
    • 0020269426 scopus 로고
    • Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden
    • STREHMEL, K. AND WEINER, R. 1982. Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden. Computing 29, 2, 153-165.
    • (1982) Computing , vol.29 , Issue.2 , pp. 153-165
    • STREHMEL, K.1    WEINER, R.2
  • 29
    • 0023173609 scopus 로고
    • B-convergence results for linearly implicit one step methods
    • STREHMEL, K. AND WEINER, R. 1987. B-convergence results for linearly implicit one step methods. BIT 27, 264-281.
    • (1987) BIT 27 , pp. 264-281
    • STREHMEL, K.1    WEINER, R.2
  • 30
    • 33947612168 scopus 로고
    • Construction of Integration Formulas for Initial Value Problems
    • North-Holland, Amsterdam, The Netherlands
    • VAN DER HOUWEN, P. J. 1977. Construction of Integration Formulas for Initial Value Problems. North-Holland Series in Applied Mathematics and Mechanics, Vol. 19. North-Holland, Amsterdam, The Netherlands.
    • (1977) North-Holland Series in Applied Mathematics and Mechanics , vol.19
    • VAN DER HOUWEN, P.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.