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Volumn 34, Issue 2, 2000, Pages 261-274

Extended explicit Bel'tyukov pairs of orders 4 and 5 for Volterra integral equations of the second kind

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; PROBLEM SOLVING; RUNGE KUTTA METHODS;

EID: 0034228946     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00132-4     Document Type: Article
Times cited : (5)

References (12)
  • 1
    • 0023329035 scopus 로고
    • A new theoretical approach to runge-kutta methods
    • [1] P. Albrecht, A new theoretical approach to Runge-Kutta methods, SIAM J. Numer. Anal. 24 (1987) 391-406.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 391-406
    • Albrecht, P.1
  • 2
    • 0007128862 scopus 로고
    • On step size control for volterra integral equations
    • Birkhäuser, Basel
    • [2] H. Arndt, On step size control for Volterra integral equations, in: International Series of Numerical Mathematics, Vol. 67, Birkhäuser, Basel, 1983, pp. 9-17.
    • (1983) International Series of Numerical Mathematics , vol.67 , pp. 9-17
    • Arndt, H.1
  • 3
    • 0001178161 scopus 로고
    • The numerical solution of nonlinear volterra integral equations of the second kind by collocation and iterated collocation methods
    • [3] J.G. Blom, H. Brunner, The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods, SIAM J. Sci. Statist. Comput. 8 (5) (1987) 806-830.
    • (1987) SIAM J. Sci. Statist. Comput. , vol.8 , Issue.5 , pp. 806-830
    • Blom, J.G.1    Brunner, H.2
  • 4
    • 84966198465 scopus 로고
    • Runge-kutta theory for volterra integral equations of the second kind
    • [4] H. Brunner, E. Hairer, S.P. Nørsett, Runge-Kutta theory for Volterra integral equations of the second kind, Math. Comp. 39 (1982) 147-163.
    • (1982) Math. Comp. , vol.39 , pp. 147-163
    • Brunner, H.1    Hairer, E.2    Nørsett, S.P.3
  • 5
    • 0003213842 scopus 로고
    • The numerical solution of volterra equations
    • North-Holland, Amsterdam
    • [5] H. Brunner, P.J. van der Houwen, The Numerical Solution of Volterra Equations, CWI Monographs, Vol. 3, North-Holland, Amsterdam, 1986.
    • (1986) CWI Monographs , vol.3
    • Brunner, H.1    Van Der Houwen, P.J.2
  • 7
    • 0007138781 scopus 로고
    • The order of convergence of general linear methods for ordinary differential equations
    • [7] G.J. Cooper, The order of convergence of general linear methods for ordinary differential equations, SIAM J. Numer. Anal. 15 (1978) 643-661.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 643-661
    • Cooper, G.J.1
  • 8
    • 0007139297 scopus 로고
    • Extended volterra-runge-kutta methods
    • C.T.H. Baker and C.F. Miller (Eds.)
    • [8] E. Hairer, Extended Volterra-Runge-Kutta methods, in: C.T.H. Baker and C.F. Miller (Eds.), Treatment of Integral Equations by Numerical Methods, 1982, pp. 221-231.
    • (1982) Treatment of Integral Equations by Numerical Methods , pp. 221-231
    • Hairer, E.1
  • 9
    • 0026216091 scopus 로고
    • Numerical comparisons of some explicit runge-kutta pairs of orders 4 through 8
    • [9] P.W. Sharp, Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8, Trans. Math. Software 17 (1991) 387-409.
    • (1991) Trans. Math. Software , vol.17 , pp. 387-409
    • Sharp, P.W.1
  • 10
    • 85031561741 scopus 로고    scopus 로고
    • Some extended bel'tyukov pairs for solving volterra equations of the second kind
    • accepted
    • [10] P.W. Sharp, J.H. Verner, Some extended Bel'tyukov pairs for solving Volterra equations of the second kind, SIAM J. Numer. Anal., accepted.
    • SIAM J. Numer. Anal.,
    • Sharp, P.W.1    Verner, J.H.2
  • 11
    • 0027683528 scopus 로고
    • Differentiable interpolants for high-order runge-kutta methods
    • [11] J.H. Verner, Differentiable interpolants for high-order Runge-Kutta methods, SIAM J. Numer. Anal. 30 (1993) 1446-1466.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1446-1466
    • Verner, J.H.1
  • 12
    • 0030283684 scopus 로고    scopus 로고
    • High-order explicit runge-kutta pairs with low stage order
    • [12] J.H. Verner, High-order explicit Runge-Kutta pairs with low stage order, Appl. Numer. Math. 22 (1996) 345-357.
    • (1996) Appl. Numer. Math. , vol.22 , pp. 345-357
    • Verner, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.