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  • Articles  (221)
  • Other Sources
  • Engineering  (198)
  • CR: 5.17  (23)
  • 1985-1989
  • 1980-1984  (221)
  • 1980  (221)
  • Mathematics  (221)
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  • Articles  (221)
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  • 1985-1989
  • 1980-1984  (221)
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  • 1
    Electronic Resource
    Electronic Resource
    On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 235-246 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of extended backward differentiation formulae suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is derived. An algorithm is described whereby the required solution is predicted using a conventional backward differentiation scheme and then corrected using an extended backward differentiation scheme of higher order. This approach allows us to developL-stable schemes of order up to 4 andL(α)-stable schemes of order up to 9. An algorithm based on the integration formulae derived in this paper is illustrated by some numerical examples and it is shown that it is often superior to certain existing algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396701
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  • 2
    Electronic Resource
    Electronic Resource
    An approximation theorem for second-order evolution equations (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 127-142 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 34G05, 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos τ for τ≧0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396311
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  • 3
    Electronic Resource
    Electronic Resource
    Méthodes multipas pour des équations paraboliques non linéaires (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 143-162 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M15, 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study the error due to the discretization in time of a nonlinear parabolic problem by a multistep method. Error estimates are obtained if the method is of the orderp (p〉1) and stronglyA(Θ)-stable $$\left( {0〈 \Theta〈 \frac{\pi }{2}} \right)$$ . The method is also applied to the Navier-Stokes equations in two dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396312
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  • 4
    Electronic Resource
    Electronic Resource
    Enlarging the domain of convergence for multiple shooting by the homotopy method (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 231-240 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The homotopy method is a frequently used technique in overcoming the local convergence nature of multiple shooting. In this paper sufficient conditions are given that guarantee the homotopy process to be feasible. The results are applicable to a class of two-point boundary value problems. Finally, the numerical solution of two practical problems arising in physiology is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396319
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  • 5
    Electronic Resource
    Electronic Resource
    Une méthode multipas implicite-explicite pour l'approximation des équations d'évolution paraboliques (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 257-276 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65M10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Résumé Considérons une équation d'évolution parabolique linéaire associée à un opérateur linéaireA(t) dépendant du tempst. Nous développons dans cet article une méthode de discrétisation, basée sur les méthodes linéaires à pas multiples, traitant de manière implicite une partie de l'opérateurA(t) indépendante du temps, l'autre partie est traitée de manière explicite. Nous étudions la stabilité et la convergence de cette méthode.
    Notes: Summary Let us consider a linear parabolic equation which is associated with a time dependent operatorA(t). In this paper, we present a method, which is founded on linear multistep methods, which discretize a time-independent part of the operatorA(t) in an implicit way, and the other part in an explicit way. We study stability and convergence for this method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396412
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  • 6
    Electronic Resource
    Electronic Resource
    Mixed finite elements in ℝ3 (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 315-341 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present here some new families of non conforming finite elements in ℝ3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396415
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  • 7
    Electronic Resource
    Electronic Resource
    A mixed finite element approximation of the Navier-Stokes equations (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 381-404 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study in this paper the convergence of a new mixed finite element approximation of the Navier-Stokes equations. This approximation uses low order Lagrange elements, leads to optimal order of convergence for the velocity and the pressure, and induces an efficient numerical algorithm for the solution of this problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399007
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  • 8
    Electronic Resource
    Electronic Resource
    Die mehrstellenformeln für den Laplaceoperator (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 171-187 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Difference methods for the numerical solution of linear partial differential equations may often be improved by using a weighted right hand side instead of the original right hand side of the differential equation. Difference formulas, for which that is possible, are called “Mehrstellenformeln’ or Hermitian formulas. In this paper the Hermitian formulas for the approximation of Laplace's operator are characterized by a very simple condition. We prove, that in two-dimensional case for a Hermitian formula of ordern at leastn+3 discretization points are necessary. We give examples of such optimal formulas of arbitrary high-order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396058
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  • 9
    Electronic Resource
    Electronic Resource
    Effective computation of periodic orbits and bifurcation diagrams in delay equations (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 457-467 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05, 65Q05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary By employing a numerical method which uses only rather classical tools of Numerical Analysis such as Newton's method and routines for ordinary differential equations, unstable periodic solutions of differential-difference equations can be computed. The method is applied to determine bifurcation diagrams with backward bifurcation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403681
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  • 10
    Electronic Resource
    Electronic Resource
    A finite element method for the Tricomi problem (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 13-20 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): primary 65M05 ; 65M10 ; 65M15 ; secondary: 35M05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider the numerical solution of the Tricomi problem. Using a weak formulation based on different spaces of test and trial functions, we construct a new Galerkin procedure for the Tricomi problem. Existence, uniqueness, and uniform stability of the approximate solution is proven, and a priori error bounds are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396366
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