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Volumn 44, Issue 3, 2004, Pages 557-570

Unconditionally stable general linear methods for ordinary differential equations

Author keywords

general linear methods; inherent Runge Kutta stability; unconditional stability

Indexed keywords


EID: 8144230572     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:BITN.0000046804.67936.06     Document Type: Article
Times cited : (13)

References (20)
  • 1
    • 38249003919 scopus 로고
    • Diagonally-implicit multi-stage integration methods
    • J. C. Butcher, Diagonally-implicit multi-stage integration methods, Appl. Numer. Math., 11 (1993), pp. 347-363.
    • (1993) Appl. Numer. Math. , vol.11 , pp. 347-363
    • Butcher, J.C.1
  • 2
    • 0036441445 scopus 로고    scopus 로고
    • Stability of numerical methods for ordinary differential equations
    • J. C. Butcher and A. D. Heard, Stability of numerical methods for ordinary differential equations, Numer. Algorithms, 31 (2002), pp. 75-85.
    • (2002) Numer. Algorithms , vol.31 , pp. 75-85
    • Butcher, J.C.1    Heard, A.D.2
  • 3
    • 0042318570 scopus 로고    scopus 로고
    • A reliable error estimation for DIMSIMs
    • J. C. Butcher and Z. Jackiewicz, A reliable error estimation for DIMSIMs, BIT, 41 (2001), pp. 656-665.
    • (2001) BIT , vol.41 , pp. 656-665
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 4
    • 0036441464 scopus 로고    scopus 로고
    • Error estimation for Nordsieck methods
    • J. C. Butcher and Z. Jackiewicz, Error estimation for Nordsieck methods, Numer. Algorithms, 31 (2002), pp. 75-85.
    • (2002) Numer. Algorithms , vol.31 , pp. 75-85
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 5
    • 0345060035 scopus 로고    scopus 로고
    • A new approach to error estimation for general linear methods
    • J. C. Butcher and Z. Jackiewicz, A new approach to error estimation for general linear methods, Numer. Math., 95 (2003), pp. 487-502.
    • (2003) Numer. Math. , vol.95 , pp. 487-502
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 6
    • 4043085577 scopus 로고    scopus 로고
    • Construction of general linear methods with Runge-Kutta stability properties
    • J. C. Butcher and Z. Jackiewicz, Construction of general linear methods with Runge-Kutta stability properties, Numer. Algorithms, 36 (2004), pp. 53-72.
    • (2004) Numer. Algorithms , vol.36 , pp. 53-72
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 7
    • 0031559380 scopus 로고    scopus 로고
    • A nonlinear optimization approach to the construction of general linear methods of high order
    • J. C. Butcher, Z. Jackiewicz, and H. D. Mittelmann, A nonlinear optimization approach to the construction of general linear methods of high order, J. Comp. Appl. Math., 81 (1997), pp. 181-196.
    • (1997) J. Comp. Appl. Math. , vol.81 , pp. 181-196
    • Butcher, J.C.1    Jackiewicz, Z.2    Mittelmann, H.D.3
  • 8
    • 4043179733 scopus 로고    scopus 로고
    • The construction of practical general linear methods
    • J. C. Butcher and W. M. Wright, The construction of practical general linear methods, BIT, 43 (2003), pp. 695-721.
    • (2003) BIT , vol.43 , pp. 695-721
    • Butcher, J.C.1    Wright, W.M.2
  • 9
    • 0347770774 scopus 로고    scopus 로고
    • On the asymptotic properties of a family of matrices
    • N. Guglielmi and M. Zennaro, On the asymptotic properties of a family of matrices, Linear Algebra Appl., 322 (2001), pp. 169-192.
    • (2001) Linear Algebra Appl. , vol.322 , pp. 169-192
    • Guglielmi, N.1    Zennaro, M.2
  • 10
    • 0035636058 scopus 로고    scopus 로고
    • On the zero-stability of variable stepsize multistep methods: The spectral radius approach
    • N. Guglielmi and M. Zennaro, On the zero-stability of variable stepsize multistep methods: the spectral radius approach, Numer. Math., 88 (2001), pp. 445-458.
    • (2001) Numer. Math. , vol.88 , pp. 445-458
    • Guglielmi, N.1    Zennaro, M.2
  • 12
    • 0036679991 scopus 로고    scopus 로고
    • Implementation of DIMSIMs for stiff differential systems
    • Z. Jackiewicz, Implementation of DIMSIMs for stiff differential systems, Appl. Numer. Math., 42 (2002), pp. 251-267.
    • (2002) Appl. Numer. Math. , vol.42 , pp. 251-267
    • Jackiewicz, Z.1
  • 13
    • 2442573699 scopus 로고    scopus 로고
    • Construction of highly stable two-step W-methods for ordinary differential equations
    • Z. Jackiewicz, H. Podhaisky, and R. Weiner, Construction of highly stable two-step W-methods for ordinary differential equations, J. Comp. Appl. Math., 167 (2004), pp. 389-403.
    • (2004) J. Comp. Appl. Math. , vol.167 , pp. 389-403
    • Jackiewicz, Z.1    Podhaisky, H.2    Weiner, R.3
  • 14
    • 0011895293 scopus 로고
    • Multistep methods are essentially one step methods
    • U. Kirchgraber, Multistep methods are essentially one step methods, Numer. Math., 48 (1986), pp. 85-90.
    • (1986) Numer. Math. , vol.48 , pp. 85-90
    • Kirchgraber, U.1
  • 15
    • 2442596454 scopus 로고    scopus 로고
    • Ph.D. Thesis, Martin-Luther-Universität, Halle-Wittenberg
    • H. Podhaisky, Parallele Zweischritt-W-Methoden, Ph.D. Thesis, Martin-Luther-Universität, Halle-Wittenberg, 2002.
    • (2002) Parallele Zweischritt-W-Methoden
    • Podhaisky, H.1
  • 16
    • 0036679945 scopus 로고    scopus 로고
    • Design, analysis and testing of some parallel two-step W-methods for stiff systems
    • H. Podhaisky, B. A. Schmitt, and R. Weiner, Design, analysis and testing of some parallel two-step W-methods for stiff systems, Appl. Numer. Math., 42 (2002), pp. 381-395.
    • (2002) Appl. Numer. Math. , vol.42 , pp. 381-395
    • Podhaisky, H.1    Schmitt, B.A.2    Weiner, R.3
  • 17
    • 0021505022 scopus 로고
    • Error estimators for stiff differential equations
    • L. F. Shampine and L. S. Baca, Error estimators for stiff differential equations, J. Comput. Appl. Math., 11 (1984), pp. 197-207.
    • (1984) J. Comput. Appl. Math. , vol.11 , pp. 197-207
    • Shampine, L.F.1    Baca, L.S.2
  • 18
    • 21144463722 scopus 로고
    • General linear methods: Connection to one step methods and invariant curves
    • D. Stoffer, General linear methods: Connection to one step methods and invariant curves, Numer. Math., 64 (1993), pp. 395-408.
    • (1993) Numer. Math. , vol.64 , pp. 395-408
    • Stoffer, D.1
  • 19
    • 0031331907 scopus 로고    scopus 로고
    • On the construction of error estimators for implicit Runge-Kutta methods
    • J. J. B. de Swart and G. Söderlind, On the construction of error estimators for implicit Runge-Kutta methods, J. Comput. Appl. Math., 86 (1997), pp. 347-358.
    • (1997) J. Comput. Appl. Math. , vol.86 , pp. 347-358
    • De Swart, J.J.B.1    Söderlind, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.