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Volumn 36, Issue 10-12, 1998, Pages 269-284

Boundary value methods: The third way between linear multistep and Runge-Kutta methods

Author keywords

Boundary value methods; Discrete boundary value problems; Linear multistep formulae; Numerical methods for ODEs

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; MATHEMATICAL TRANSFORMATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; RUNGE KUTTA METHODS;

EID: 0032204862     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0898-1221(98)80028-x     Document Type: Article
Times cited : (60)

References (22)
  • 1
    • 33747690246 scopus 로고
    • Math. Tables, British Association for the Advancement of Sciences, Cambridge University Press
    • J.C.P. Miller, Bessel Functions, Part II, Math. Tables, Vol. X, British Association for the Advancement of Sciences, Cambridge University Press, (1952).
    • (1952) Bessel Functions, Part Ii , vol.10
    • Miller, J.C.P.1
  • 2
    • 0029721294 scopus 로고    scopus 로고
    • Convergence and stability of boundary value methods for ordinary differential equations
    • L. Brugnano and D. Trigiante, Convergence and stability of boundary value methods for ordinary differential equations, J. Comp. Appl. Math. 66, 97-109 (1996).
    • (1996) J. Comp. Appl. Math. , vol.66 , pp. 97-109
    • Brugnano, L.1    Trigiante, D.2
  • 4
    • 0003034563 scopus 로고
    • The symplectic methods for the computation of Hamiltonian equations
    • Shanghai, (March 1986), Edited by Zhu You-lan Gu Ben-yu, Lecture Notes in Math., Springer, Berlin
    • st Chinese Conference on Numerical Methods of PDE's, Shanghai, (March 1986), Volume 1297, (Edited by Zhu You-lan and Gu Ben-yu), Lecture Notes in Math., Springer, Berlin, (1987).
    • (1987) st Chinese Conference on Numerical Methods of Pde's , vol.1297
    • Kang, F.1    Meng-Zhao, Q.2
  • 5
    • 84971897259 scopus 로고
    • Symplectic integrators for Hamiltonian problems: An overview
    • J.M. Sanz-Serna, Symplectic integrators for Hamiltonian problems: An overview, Acta Numerica, 243-286 (1991).
    • (1991) Acta Numerica , pp. 243-286
    • Sanz-Serna, J.M.1
  • 6
    • 0038041190 scopus 로고
    • The canonicity of mappings generated by Runge-Kutta type methods when integrating the systems ẍ = -∂U/∂x
    • Y.B. Suris, The canonicity of mappings generated by Runge-Kutta type methods when integrating the systems ẍ = -∂U/∂x, U.S.S.R. Comput. Maths. Math. Phys. 29, 138-144 (1989).
    • (1989) U.S.S.R. Comput. Maths. Math. Phys. , vol.29 , pp. 138-144
    • Suris, Y.B.1
  • 7
    • 0040260398 scopus 로고    scopus 로고
    • Essentially symplectic boundary value methods for linear Hamiltonian systems
    • L. Brugnano, Essentially symplectic boundary value methods for linear Hamiltonian systems, J. Comput. Math. 15, 233-252 (1997).
    • (1997) J. Comput. Math. , vol.15 , pp. 233-252
    • Brugnano, L.1
  • 9
    • 0039639872 scopus 로고
    • High order multistep methods for boundary value problems
    • L. Brugnano and D. Trigiante, High order multistep methods for boundary value problems, Appl. Numer. Math. 18, 79-94 (1995).
    • (1995) Appl. Numer. Math. , vol.18 , pp. 79-94
    • Brugnano, L.1    Trigiante, D.2
  • 10
    • 0039076592 scopus 로고    scopus 로고
    • Block boundary value methods for linear Hamiltonian systems
    • L. Brugnano and D. Trigiante, Block boundary value methods for linear Hamiltonian systems, Jour. of Appl. Math. 81, 49-68 (1997).
    • (1997) Jour. of Appl. Math. , vol.81 , pp. 49-68
    • Brugnano, L.1    Trigiante, D.2
  • 11
    • 0040260395 scopus 로고
    • A boundary value approach to the numerical solution of ODEs by multistep methods
    • P. Amodio and F. Mazzia, A boundary value approach to the numerical solution of ODEs by multistep methods, Jour. of Difference Eq. and Appl. 1, 353-367 (1995).
    • (1995) Jour. of Difference Eq. and Appl. , vol.1 , pp. 353-367
    • Amodio, P.1    Mazzia, F.2
  • 13
    • 0011566457 scopus 로고
    • Convergence and stability in the numerical integration of ordinary differential equations
    • G. Dahlquist, Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand. 4, 33-53 (1956).
    • (1956) Math. Scand. , vol.4 , pp. 33-53
    • Dahlquist, G.1
  • 14
    • 0031188156 scopus 로고    scopus 로고
    • A new mesh selection strategy for ODEs
    • L. Brugnano and D. Trigiante, A new mesh selection strategy for ODEs, Appl. Numer. Math. 24, 1-21 (1997).
    • (1997) Appl. Numer. Math. , vol.24 , pp. 1-21
    • Brugnano, L.1    Trigiante, D.2
  • 15
    • 0031078576 scopus 로고    scopus 로고
    • Parallel implementation of block boundary value methods for ODEs
    • P. Amodio and L. Brugnano, Parallel implementation of block boundary value methods for ODEs, J. Comp. Appl. Math. 78, 197-211 (1997).
    • (1997) J. Comp. Appl. Math. , vol.78 , pp. 197-211
    • Amodio, P.1    Brugnano, L.2
  • 18
    • 84966215337 scopus 로고
    • Boundary value techniques for initial value problems in ordinary differential equations
    • A.O.H. Axelsson and J.G. Verwer, Boundary value techniques for initial value problems in ordinary differential equations, Math. Comp. 45, 153-171 (1985).
    • (1985) Math. Comp. , vol.45 , pp. 153-171
    • Axelsson, A.O.H.1    Verwer, J.G.2
  • 19
    • 0041623773 scopus 로고
    • Tridiagonal matrices and numerical solution of ordinary differential equations
    • World Scientific Series in Applicable Analysis
    • L. Brugnano and D. Trigiante, Tridiagonal matrices and numerical solution of ordinary differential equations, In Contributions in Numerical Mathematics, Volume 2, pp. 71-83, World Scientific Series in Applicable Analysis, (1993).
    • (1993) Contributions in Numerical Mathematics , vol.2 , pp. 71-83
    • Brugnano, L.1    Trigiante, D.2
  • 21
    • 84950209519 scopus 로고
    • Stability and convergence of boundary value methods for solving ODE
    • P. Marzulli and D. Trigiante, Stability and convergence of boundary value methods for solving ODE, Jour. of Difference Eq. and Appl. 1, 45-55 (1995).
    • (1995) Jour. of Difference Eq. and Appl. , vol.1 , pp. 45-55
    • Marzulli, P.1    Trigiante, D.2
  • 22
    • 0042625758 scopus 로고
    • Boundary value techniques for the numerical solution of certain initial value problems in ordinary differential equations
    • R.A. Usmani, Boundary value techniques for the numerical solution of certain initial value problems in ordinary differential equations, J. ACM 3, 287-295 (1966).
    • (1966) J. ACM , vol.3 , pp. 287-295
    • Usmani, R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.