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Volumn 27, Issue 4, 2007, Pages 798-817

A family of A-stable Runge-Kutta collocation methods of higher order for initial-value problems

Author keywords

A stability; Initial value problems; Runge Kutta collocation methods

Indexed keywords

INITIAL VALUE PROBLEMS; NUMERICAL METHODS;

EID: 35348868776     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drl040     Document Type: Article
Times cited : (53)

References (28)
  • 1
    • 0031367176 scopus 로고    scopus 로고
    • A note on the efficient implementation of implicit methods for ODEs
    • AMODIO, P. & BRUGNANO, L. (1997) A note on the efficient implementation of implicit methods for ODEs. J. Comput. Appl. Math., 87, 1-9.
    • (1997) J. Comput. Appl. Math , vol.87 , pp. 1-9
    • AMODIO, P.1    BRUGNANO, L.2
  • 3
    • 4944240756 scopus 로고    scopus 로고
    • Barycentric Lagrange interpolation
    • BERRUT, J. P. & TREFETHEN, L. N. (2004) Barycentric Lagrange interpolation. SIAM Rev., 46, 501-517.
    • (2004) SIAM Rev , vol.46 , pp. 501-517
    • BERRUT, J.P.1    TREFETHEN, L.N.2
  • 6
    • 23644439948 scopus 로고    scopus 로고
    • General linear methods
    • BUTCHER, J. C. (1996) General linear methods. Comput. Math. Appl., 31, 105-112.
    • (1996) Comput. Math. Appl , vol.31 , pp. 105-112
    • BUTCHER, J.C.1
  • 8
  • 9
    • 0012149379 scopus 로고
    • An iteration scheme for implicit Runge-Kutta methods
    • COOPER, G. J. & BUTCHER, J. C. (1983) An iteration scheme for implicit Runge-Kutta methods. IMA J. Numer. Anal., 3, 127-140.
    • (1983) IMA J. Numer. Anal , vol.3 , pp. 127-140
    • COOPER, G.J.1    BUTCHER, J.C.2
  • 12
    • 35348854991 scopus 로고    scopus 로고
    • HAIRER, E. & WANNER, G. (1996) Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Berlin, Germany: Springer.
    • HAIRER, E. & WANNER, G. (1996) Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Berlin, Germany: Springer.
  • 16
    • 0032184119 scopus 로고    scopus 로고
    • Solving ordinary differential equations by generalized Adams methods: Properties and implementaion techniques
    • IAVERNARO, F. & MAZZIA, F. (1998) Solving ordinary differential equations by generalized Adams methods: properties and implementaion techniques. Appl. Numer. Math., 28, 107-126.
    • (1998) Appl. Numer. Math , vol.28 , pp. 107-126
    • IAVERNARO, F.1    MAZZIA, F.2
  • 17
    • 2442573699 scopus 로고    scopus 로고
    • Construction of highly stable two-step W-methods for ordinary differential equations
    • JACKIEWICZ, Z., PODHAISKY, H. & WEINER, R. (2004) Construction of highly stable two-step W-methods for ordinary differential equations. J. Comput. Appl. Math., 167, 389-403.
    • (2004) J. Comput. Appl. Math , vol.167 , pp. 389-403
    • JACKIEWICZ, Z.1    PODHAISKY, H.2    WEINER, R.3
  • 20
    • 28144459236 scopus 로고    scopus 로고
    • Test set for initial value problems solvers
    • Technical Report 40/2003. Department of Mathematics, University of Bari
    • MAZZIA, F. & IAVERNARO, F. (2003) Test set for initial value problems solvers. Technical Report 40/2003. Department of Mathematics, University of Bari.
    • (2003)
    • MAZZIA, F.1    IAVERNARO, F.2
  • 21
    • 0007013992 scopus 로고
    • C-polynomials for rational approximation to the exponential function
    • NØRSETT, S. P. (1975) C-polynomials for rational approximation to the exponential function. Numer. Math., 25, 39-56.
    • (1975) Numer. Math , vol.25 , pp. 39-56
    • NØRSETT, S.P.1
  • 22
    • 0013352563 scopus 로고
    • A family of implicit Chebyshev methods for the numerical integration of second-order differential equations
    • PANOWSKY, J. & RICHARDSON, D. L. (1988) A family of implicit Chebyshev methods for the numerical integration of second-order differential equations. J. Comput. Appl. Math., 23, 35-51.
    • (1988) J. Comput. Appl. Math , vol.23 , pp. 35-51
    • PANOWSKY, J.1    RICHARDSON, D.L.2
  • 23
    • 84968497765 scopus 로고
    • On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations
    • PROTHERO, A. & ROBINSON, A. (1974) On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations. Math. Comput., 28, 145-162.
    • (1974) Math. Comput , vol.28 , pp. 145-162
    • PROTHERO, A.1    ROBINSON, A.2
  • 24
    • 27744566328 scopus 로고    scopus 로고
    • The accuracy of the Chebyshev differencing method for analytic functions
    • REDDY, S. C. & WEIDEMAN, J. A. (2005) The accuracy of the Chebyshev differencing method for analytic functions. SIAM J. Numer. Anal., 42, 2176-2187.
    • (2005) SIAM J. Numer. Anal , vol.42 , pp. 2176-2187
    • REDDY, S.C.1    WEIDEMAN, J.A.2
  • 25
    • 0038976122 scopus 로고    scopus 로고
    • Runge-Kutta schemes for Hamiltonian systems
    • SANZ-SERNA, J. M. (1998) Runge-Kutta schemes for Hamiltonian systems. BIT, 28, 877-883.
    • (1998) BIT , vol.28 , pp. 877-883
    • SANZ-SERNA, J.M.1
  • 27
    • 0042094921 scopus 로고    scopus 로고
    • An efficient algorithm for solving stiff ordinary differential equations
    • STABROWSKI, M. M. (1997) An efficient algorithm for solving stiff ordinary differential equations. Simul Pract. Theory, 5, 333-344.
    • (1997) Simul Pract. Theory , vol.5 , pp. 333-344
    • STABROWSKI, M.M.1
  • 28
    • 0042785930 scopus 로고    scopus 로고
    • Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order diferential equations
    • VIGO-AGUIAR, J. & RAMOS, H. (2003) Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order diferential equations. J. Comput. Appl. Math., 158, 187-211.
    • (2003) J. Comput. Appl. Math , vol.158 , pp. 187-211
    • VIGO-AGUIAR, J.1    RAMOS, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.