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Volumn 7, Issue 1-2, 1997, Pages 5-26

Parallel ODE solvers based on block BVMs

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EID: 0031502534     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018926314954     Document Type: Article
Times cited : (13)

References (45)
  • 2
    • 0009193978 scopus 로고
    • Parallel factorizations and parallel solvers for tridiagonal linear systems
    • P. Amodio and L. Brugnano, Parallel factorizations and parallel solvers for tridiagonal linear systems, Linear Algebra Appl. 172 (1992) 347-364.
    • (1992) Linear Algebra Appl. , vol.172 , pp. 347-364
    • Amodio, P.1    Brugnano, L.2
  • 3
    • 0042118621 scopus 로고    scopus 로고
    • Parallel implementation of block boundary value methods for ODEs
    • to appear
    • P. Amodio and L. Brugnano, Parallel implementation of block boundary value methods for ODEs, J. Comput. Math. Appl., to appear.
    • J. Comput. Math. Appl.
    • Amodio, P.1    Brugnano, L.2
  • 4
    • 0027607183 scopus 로고
    • Parallel factorizations for tridiagonal matrices
    • P. Amodio, L. Brugnano and T. Politi, Parallel factorizations for tridiagonal matrices, SIAM J. Numer. Anal. 30 (1993) 813-823.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 813-823
    • Amodio, P.1    Brugnano, L.2    Politi, T.3
  • 5
    • 0042619755 scopus 로고
    • Variable step boundary value methods based on reverse Adams schemes and their grid redistribution
    • P. Amodio, W. L. Golik and F. Mazzia, Variable step boundary value methods based on reverse Adams schemes and their grid redistribution, Appl. Numer. Math. 18 (1995) 5-22.
    • (1995) Appl. Numer. Math. , vol.18 , pp. 5-22
    • Amodio, P.1    Golik, W.L.2    Mazzia, F.3
  • 6
    • 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, J. Differential Equations Appl. 1 (1995) 353-367.
    • (1995) J. Differential Equations Appl. , vol.1 , pp. 353-367
    • Amodio, P.1    Mazzia, F.2
  • 7
    • 21344497804 scopus 로고
    • Boundary value methods for the solution of differential-algebraic equations
    • P. Amodio and F. Mazzia, Boundary value methods for the solution of differential-algebraic equations, Numer. Math. 66 (1994) 411-421.
    • (1994) Numer. Math. , vol.66 , pp. 411-421
    • Amodio, P.1    Mazzia, F.2
  • 8
    • 0039541617 scopus 로고
    • A parallel Gauss-Seidel method for block tridiagonal linear systems
    • P. Amodio and F. Mazzia, A parallel Gauss-Seidel method for block tridiagonal linear systems, SIAM J. Sci. Comput. 16 (1995) 1451-1461.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 1451-1461
    • Amodio, P.1    Mazzia, F.2
  • 9
    • 0030142876 scopus 로고    scopus 로고
    • Parallel block preconditioning for the solution of boundary value methods
    • P. Amodio and F. Mazzia, Parallel block preconditioning for the solution of boundary value methods, J. Comput. Appl. Math. 69 (1996) 191-206.
    • (1996) J. Comput. Appl. Math. , vol.69 , pp. 191-206
    • Amodio, P.1    Mazzia, F.2
  • 10
    • 0040133109 scopus 로고    scopus 로고
    • Parallel iterative solvers for boundary value methods
    • P. Amodio and F. Mazzia, Parallel iterative solvers for boundary value methods, Math. Comput. Modelling 23(7) (1996) 29-43.
    • (1996) Math. Comput. Modelling , vol.23 , Issue.7 , pp. 29-43
    • Amodio, P.1    Mazzia, F.2
  • 11
    • 0007152722 scopus 로고
    • Stability of some boundary value methods for the solution of initial value problems
    • P. Amodio, F. Mazzia and D. Trigiante, Stability of some boundary value methods for the solution of initial value problems, BIT 33 (1993) 434-451.
    • (1993) BIT , vol.33 , pp. 434-451
    • Amodio, P.1    Mazzia, F.2    Trigiante, D.3
  • 12
    • 0030621835 scopus 로고    scopus 로고
    • A cyclic reduction approach to the numerical solution of boundary value ODEs
    • to appear
    • P. Amodio and M. Paprzycki, A cyclic reduction approach to the numerical solution of boundary value ODEs, SIAM J. Sci. Comput. 18 (1997), to appear.
    • (1997) SIAM J. Sci. Comput. , vol.18
    • Amodio, P.1    Paprzycki, M.2
  • 13
    • 0027204442 scopus 로고
    • A parallel direct method for solving initial value problems
    • P. Amodio and D. Trigiante, A parallel direct method for solving initial value problems, Appl. Numer. Math. 11 (1993) 85-93.
    • (1993) Appl. Numer. Math. , vol.11 , pp. 85-93
    • Amodio, P.1    Trigiante, D.2
  • 15
    • 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 (1985) 153-171.
    • (1985) Math. Comp. , vol.45 , pp. 153-171
    • Axelsson, A.O.H.1    Verwer, J.G.2
  • 16
    • 0040260398 scopus 로고    scopus 로고
    • Essentially symplectic boundary value methods for linear Hamiltonian systems
    • to appear
    • L. Brugnano, Essentially symplectic boundary value methods for linear Hamiltonian systems, J. Comput. Math., to appear.
    • J. Comput. Math.
    • Brugnano, L.1
  • 17
    • 0043120553 scopus 로고    scopus 로고
    • Boundary value methods for the numerical approximation of ordinary differential equations
    • Rousse, 24-27 June 1996, Lecture Notes in Computer Science, to appear
    • L. Brugnano, Boundary value methods for the numerical approximation of ordinary differential equations, in: Proc. 1st Workshop on Numerical Analysis and Applications, Rousse, 24-27 June 1996, Lecture Notes in Computer Science, to appear.
    • Proc. 1st Workshop on Numerical Analysis and Applications
    • Brugnano, L.1
  • 19
    • 0041623773 scopus 로고
    • Tridiagonal matrices and numerical solution of ordinary differential equations
    • L. Brugnano and D. Trigiante, Tridiagonal matrices and numerical solution of ordinary differential equations, WSSIA 2 (1993) 71-83.
    • (1993) WSSIA , vol.2 , pp. 71-83
    • Brugnano, L.1    Trigiante, D.2
  • 20
    • 0027700808 scopus 로고
    • Stability properties of some BVM methods
    • L. Brugnano and D. Trigiante, Stability properties of some BVM methods, Appl. Numer. Math. 13 (1993) 291-304.
    • (1993) Appl. Numer. Math. , vol.13 , pp. 291-304
    • Brugnano, L.1    Trigiante, D.2
  • 21
    • 0027703239 scopus 로고
    • A parallel preconditioning technique for BVM methods
    • L. Brugnano and D. Trigiante, A parallel preconditioning technique for BVM methods, Appl. Numer. Math. 13 (1993) 277-290.
    • (1993) Appl. Numer. Math. , vol.13 , pp. 277-290
    • Brugnano, L.1    Trigiante, D.2
  • 22
    • 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. Comput. Appl. Math. 66 (1996) 97-109.
    • (1996) J. Comput. Appl. Math. , vol.66 , pp. 97-109
    • Brugnano, L.1    Trigiante, D.2
  • 23
    • 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 (1995) 79-94.
    • (1995) Appl. Numer. Math. , vol.18 , pp. 79-94
    • Brugnano, L.1    Trigiante, D.2
  • 24
    • 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, Appl. Math. Comput. 81 (1997) 49-68.
    • (1997) Appl. Math. Comput. , vol.81 , pp. 49-68
    • Brugnano, L.1    Trigiante, D.2
  • 27
    • 0032204862 scopus 로고    scopus 로고
    • Boundary value methods: The third way between linear multistep and Runge-Kutta methods
    • to appear
    • L. Brugnano and D. Trigiante, Boundary value methods: the third way between linear multistep and Runge-Kutta methods, Comput. Math. Appl., to appear.
    • Comput. Math. Appl.
    • Brugnano, L.1    Trigiante, D.2
  • 30
    • 84966223411 scopus 로고
    • An analysis of boundary value techniques for parabolic equations
    • A. Carasso and S. V. Parter, An analysis of boundary value techniques for parabolic equations, Math. Comp. 24 (1970) 315-340.
    • (1970) Math. Comp. , vol.24 , pp. 315-340
    • Carasso, A.1    Parter, S.V.2
  • 32
    • 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 (1956) 33-53.
    • (1956) Math. Scand. , vol.4 , pp. 33-53
    • Dahlquist, G.1
  • 35
    • 0030621837 scopus 로고    scopus 로고
    • Convergence and stability of multistep methods solving nonlinear initial value problems
    • to appear
    • F. Iavernaro and F. Mazzia, Convergence and stability of multistep methods solving nonlinear initial value problems, SIAM J. Sci. Comput. 18 (1997), to appear.
    • (1997) SIAM J. Sci. Comput. , vol.18
    • Iavernaro, F.1    Mazzia, F.2
  • 36
    • 38249007106 scopus 로고
    • Boundary value methods and BV-stability in the solution of initial value problems
    • L. Lopez and D. Trigiante, Boundary value methods and BV-stability in the solution of initial value problems, Appl. Numer. Math. 11 (1993) 225-239.
    • (1993) Appl. Numer. Math. , vol.11 , pp. 225-239
    • Lopez, L.1    Trigiante, D.2
  • 37
    • 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, J. Differential Equations Appl. 1 (1995) 45-55.
    • (1995) J. Differential Equations Appl. , vol.1 , pp. 45-55
    • Marzulli, P.1    Trigiante, D.2
  • 38
    • 0019677022 scopus 로고
    • Estimates for the errors in the solutions of linear boundary value problems, due to perturbations
    • R. M. M. Mattheij, Estimates for the errors in the solutions of linear boundary value problems, due to perturbations, Computing 27 (1981) 299-318.
    • (1981) Computing , vol.27 , pp. 299-318
    • Mattheij, R.M.M.1
  • 39
    • 0022031291 scopus 로고
    • Decoupling and stability of algorithms for boundary value problems
    • R. M. M. Mattheij, Decoupling and stability of algorithms for boundary value problems, SIAM Rev. 27 (1985) 1-44.
    • (1985) SIAM Rev. , vol.27 , pp. 1-44
    • Mattheij, R.M.M.1
  • 40
    • 0041819194 scopus 로고
    • Boundary value methods for initial value problems: Parallel implementation
    • F. Mazzia, Boundary value methods for initial value problems: parallel implementation, Ann. Numer. Math. 1 (1994) 439-450.
    • (1994) Ann. Numer. Math. , vol.1 , pp. 439-450
    • Mazzia, F.1
  • 42
    • 33747690246 scopus 로고
    • Bessel Functions, Part II
    • 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) Math. Tables , vol.10
    • Miller, J.C.P.1
  • 43
    • 0039022112 scopus 로고
    • Numerical solutions of second order linear difference equations
    • F. W. J. Olver, Numerical solutions of second order linear difference equations, J. Res. Nat. Bur. Standards Math, and Math. Phys. 71B (2 and 3) (1967) 111-129.
    • (1967) J. Res. Nat. Bur. Standards Math, and Math. Phys. , vol.71 B , Issue.2-3 , pp. 111-129
    • Olver, F.W.J.1
  • 44
    • 0041819204 scopus 로고    scopus 로고
    • Multipoint methods for linear Hamiltonian systems
    • Ser. Stability and Control: Theory, Methods and Applications Gordon & Breach, Reading, UK
    • D. Trigiante, Multipoint methods for linear Hamiltonian systems, in: Advances in Nonlinear Dynamics, Ser. Stability and Control: Theory, Methods and Applications (Gordon & Breach, Reading, UK, 1996).
    • (1996) Advances in Nonlinear Dynamics
    • Trigiante, D.1
  • 45
    • 21344482160 scopus 로고
    • Stable parallel elimination for boundary value ODEs
    • S. J. Wright, Stable parallel elimination for boundary value ODEs, Numer. Math. 67 (1994) 521-535.
    • (1994) Numer. Math. , vol.67 , pp. 521-535
    • Wright, S.J.1


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