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  • Artikel  (98)
  • CR: 5.17  (98)
  • Springer  (98)
  • 1980-1984  (98)
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  • Artikel  (98)
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  • 1
    Digitale Medien
    Digitale Medien
    On calculating the eigenvalues of the finite Hill's differential equation (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 255-279 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65L15 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Some methods for evaluating the characteristic exponents in connection with Newton's iteration are applied for solving the eigenvalue problem related to the finite Hill's differential equation or, in particular, Mathieu's equation. By using these methods a high accuracy is achieved, furthermore a complete error analysis, which yields rather realistic error bounds, is possible.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01390215
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  • 2
    Digitale Medien
    Digitale Medien
    A semi-implicit mid-point rule for stiff systems of ordinary differential equations (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 373-398 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65L05 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The paper introduces a new semi-implicit extrapolation method especially designed for the numerical solution of stiff systems of ordinary differential equations. The existence of a quadratic asymptotic expansion in terms of the stepsize is shown. Moreover, the new discretization is analyzed in the light of well-known stability models. The efficiency of the new integrator is clearly demonstrated by solving a series of challenging test problems including real life examples.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01418331
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  • 3
    Digitale Medien
    Digitale Medien
    Maximum-norm stability and error estimates in Galerkin methods for parabolic equations in one space variable (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 345-371 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Maximum-norm stability and error estimates of best approximation and nonsmooth data types are derived for the approximate solution of a parabolic equation in one space variable, using the continuous in time Galerkin method based on piecewise polynomial approximating functions on a quasi-uniform mesh.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01418330
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  • 4
    Digitale Medien
    Digitale Medien
    Die maximale Konsistenzordnung von Differenzenapproximationen nichtnegativer Art (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 119-123 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N10 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Many difference methods for the numerical solution of elliptic boundary value problems lead to systems of linear equations whose matrices areM-matrices and which therefore have nonnegative inverses. In this paper it is shown, that these difference methods are at most consistent of second order.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01400922
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  • 5
    Digitale Medien
    Digitale Medien
    Contractivity in the numerical solution of initial value problems (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 271-290 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65J10, 65L20, 65M10 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Consider a linear autonomous system of ordinary differential equations with the property that the norm |U(t)| of each solutionU(t) satisfies |U(t)|≦|U(0)| (t≧0). We call a numerical process for solving such a system contractive if a discrete version of this property holds for the numerical approximations. A givenk-step method is said to be unconditionally contractive if for each stepsizeh〉0 the numerical process is contractive. In this paper a general theory is given which yields necessary and sufficient conditions for unconditional contractivity. It turns out that unconditionally contractive methods are subject to an order barrierp≦1. Further the concept of a contractivity threshold is studied, which makes it possible to compare the contractivity behaviour of methods with an orderp〉1 as well. Most theoretical results in this paper are formulated for differential equations in arbitrary Banach spaces. Applications are given to numerical methods for solving ordinary as well as partial differential equations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01389573
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  • 6
    Digitale Medien
    Digitale Medien
    Split linear multistep methods for the numerical integration of stiff differential systems (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 299-310 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65L05 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A new approach to the problem of numerically integrating stiff differential systems is described. In this approach a linear multistep method (the basic method) is split into a kind of predictor-corrector scheme, where the predictor is also implicit. If this splitting is done in an appropriate manner, the modified method has considerably better stability properties than the basic method. As a result, splitting methods are particularly useful for problems where conventional integration methods experience stability difficulties. In particular some highly stable split linear multistep methods based on backward differentiation formulae are derived and a highly stable variable step implementation is proposed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01389575
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  • 7
    Digitale Medien
    Digitale Medien
    A boundary element method for a two-dimensional interface problem in electromagnetics (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 311-322 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65 N 30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper presents Galerkin approximations for solutions of two dimensional interface problems by solving corresponding boundary integral equations. These are obtained by simple layer potential operators only. Due to the strong ellipticity of the integral equations the Galerkin procedure converges with optimal order. Smoothness of the given data implies high convergence rates for the layers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01389576
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  • 8
    Digitale Medien
    Digitale Medien
    OnD-stability andB-stability (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 349-357 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS) 65L05 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper theD-stability properties of some classes of perturbed collocation methods are investigated. Among others we show the implicit Runge-Kutta methods described by Ehle-Chipman to beD-stable. We also give implicit Runge-Kutta methods that are bothD-stable andA-stable but notB-stable. Finally we indicate in what senseB-stability is stronger thanA-stability together withD-stability. The results of this paper are based on recent results of Nørsett and Wanner on perturbed collocation methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01389579
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  • 9
    Digitale Medien
    Digitale Medien
    Stability of multistep-methods on variable grids (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 359-377 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS 65L05 ; 65L07 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper is concerned with the stability of multistep methods for ordinary initial-value problems on grids with variable mesh-sizes. A necessary and sufficient condition for stability is given from which generalizations of recent results by Gear et al. and by Zlatev can be obtained as special cases. As an application the stability of the variable BDF-formulas is treated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01389580
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  • 10
    Digitale Medien
    Digitale Medien
    Norm bounds for rational matrix functions (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 379-389 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65L20 ; 15A60 ; 65M20 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary If the field of values of a matrixA is contained in the left complex halfplaneH and a functionf mapsH into the unit disc then ∥f(A)∥2≦1 by a theorem of J.v. Neumann. We prove a theorem of this type, only the field of values ofA is used for functions which are absolutely bounded by one in only part ofH. An extension can be used to show norm-stability of single step methods for stiff differential equations. The results are applicable among others to several subdiagonal Padé approximations which are notA-stable.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01389581
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