메뉴 건너뛰기




Volumn 53, Issue 2-4, 2005, Pages 323-339

Exponential Runge-Kutta methods for parabolic problems

Author keywords

Convergence bounds; Exponential collocation methods; Exponential quadrature rules; Preservation of equilibria; Semilinear parabolic problems

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; FUNCTIONS; INTEGRATION; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; NAVIER STOKES EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

EID: 14844318087     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.08.005     Document Type: Conference Paper
Times cited : (176)

References (20)
  • 3
    • 0036501083 scopus 로고    scopus 로고
    • Exponential time differencing for stiff systems
    • S.M. Cox, and P.C. Matthews 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
  • 4
    • 84985376656 scopus 로고
    • Krylov subspace approximations of eigenpairs and matrix functions in exact and computer arithmetic
    • V.L. Druskin, and L.A. Knizhnerman Krylov subspace approximations of eigenpairs and matrix functions in exact and computer arithmetic Numer. Linear Algebra Appl. 2 1995 205 217
    • (1995) Numer. Linear Algebra Appl. , vol.2 , pp. 205-217
    • Druskin, V.L.1    Knizhnerman, L.A.2
  • 5
    • 0346099850 scopus 로고
    • Verallgemeinerte Runge-Kutta Verfahren zur Lösung steifer Differentialgleichungssysteme
    • R. Bulirsch R.D. Grigorieff J. Schröder, Numerical Treatment of Differential Equations, Springer Berlin
    • A. Friedli Verallgemeinerte Runge-Kutta Verfahren zur Lösung steifer Differentialgleichungssysteme R. Bulirsch R.D. Grigorieff J. Schröder Numerical Treatment of Differential Equations Lecture Notes in Mathematics vol. 631 1978 Springer Berlin
    • (1978) Lecture Notes in Mathematics , vol.631
    • Friedli, A.1
  • 6
    • 0002171573 scopus 로고
    • Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order
    • D. Fujiwara Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order Proc. Japan Acad. 43 1967 82 86
    • (1967) Proc. Japan Acad. , vol.43 , pp. 82-86
    • Fujiwara, D.1
  • 7
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer Berlin
    • D. Henry Geometric Theory of Semilinear Parabolic Equations Lecture Notes in Mathematics vol. 840 1981 Springer Berlin
    • (1981) Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 8
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • M. Hochbruck, and Ch. Lubich On Krylov subspace approximations to the matrix exponential operator SIAM J. Numer. Anal. 34 1997 1911 1925
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, Ch.2
  • 9
    • 0002279610 scopus 로고    scopus 로고
    • Exponential integrators for large systems of differential equations
    • M. Hochbruck, Ch. Lubich, and H. Selhofer Exponential integrators for large systems of differential equations SIAM J. Sci. Comput. 19 1998 1552 1574
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1552-1574
    • Hochbruck, M.1    Lubich, Ch.2    Selhofer, H.3
  • 12
    • 0001202958 scopus 로고
    • Generalized Runge-Kutta processes for stable systems with large Lipschitz constants
    • J.D. Lawson Generalized Runge-Kutta processes for stable systems with large Lipschitz constants SIAM J. Numer. Anal. 4 1967 372 380
    • (1967) SIAM J. Numer. Anal. , vol.4 , pp. 372-380
    • Lawson, J.D.1
  • 13
    • 84968504982 scopus 로고
    • Runge-Kutta methods for parabolic equations and convolution quadrature
    • Ch. Lubich, and A. Ostermann Runge-Kutta methods for parabolic equations and convolution quadrature Math. Comp. 60 1993 105 131
    • (1993) Math. Comp. , vol.60 , pp. 105-131
    • Lubich, Ch.1    Ostermann, A.2
  • 14
    • 21844506712 scopus 로고
    • Linearly implicit time discretization of non-linear parabolic equations
    • Ch. Lubich, and A. Ostermann Linearly implicit time discretization of non-linear parabolic equations IMA J. Numer. Anal. 15 1995 555 583
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 555-583
    • Lubich, Ch.1    Ostermann, A.2
  • 15
    • 84968497603 scopus 로고
    • Runge-Kutta approximation of quasi-linear parabolic equations
    • Ch. Lubich, and A. Ostermann Runge-Kutta approximation of quasi-linear parabolic equations Math. Comp. 64 1995 601 627
    • (1995) Math. Comp. , vol.64 , pp. 601-627
    • Lubich, Ch.1    Ostermann, A.2
  • 17
    • 0346196616 scopus 로고
    • An A-stable modification of the Adams-Bashforth methods
    • J.L. Morris, Conference on the Numerical Solution of Differential Equations, Springer Berlin
    • S.P. Nørsett An A-stable modification of the Adams-Bashforth methods J.L. Morris Conference on the Numerical Solution of Differential Equations Lecture Notes in Mathematics vol. 109 1978 Springer Berlin
    • (1978) Lecture Notes in Mathematics , vol.109
    • Nørsett, S.P.1
  • 19
    • 0023173609 scopus 로고
    • B-convergence results for linearly implicit one step methods
    • K. Strehmel, and R. Weiner B-convergence results for linearly implicit one step methods BIT 27 1987 264 281
    • (1987) BIT , vol.27 , pp. 264-281
    • Strehmel, K.1    Weiner, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.