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  • Articles  (41)
  • Mathematics and Statistics  (41)
  • 2020-2022
  • 1975-1979  (41)
  • 1950-1954
  • Mathematics  (41)
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  • Articles  (41)
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  • Mathematics  (41)
  • Sociology
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  • 1
    Electronic Resource
    Electronic Resource
    Analysis of Generalised Galerkin methods in the numerical solution of elliptic equations (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 3-15 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Petrov-Galerkin projection method is outlined for the solution of the linear elliptic equation Lu = f with homogeneous boundary conditions. By choosing appropriate finite dimensional trial and test spaces, the methods of weighted residuals, collocation, and H1 Galerkin can be interpreted within the Petrov-Galerkin projection method framework.The important question of how best to choose the trial and test functions to suit a particular type of problem is then discussed. Objective criteria associated with the matrix which governs the Petrov-Galerkin numerical process are proposed.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010102
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  • 2
    Electronic Resource
    Electronic Resource
    The construction of solutions to the heat equation backward in timeDedicated to the memory of our “Doctor-Father” Professor Arthur Erdélyi. (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 32-39 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Solutions to the backwards heat equation are approximated by solutions of a pseudo-heat equation. Solutions to this modified equation are constructed by means of a fundamental solution and potential theory, and it is shown that the fundamental solution can be approximated by various expansions in special functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010104
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  • 3
    Electronic Resource
    Electronic Resource
    On the treatment of free boundary problems with the heat equation via optimal control (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 40-61 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider a free boundary problem of general type for the heat equation in one space dimension. We formulate this problem as an optimal control problem and derive necessary conditions for a solution of it. In order to compute a solution of the control problem, we apply the projection-gradient-method. Simple numerical examples illustrate the results.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010105
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  • 4
    Electronic Resource
    Electronic Resource
    The convergence of the horizontal line method for Maxwell's equations (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 101-113 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The interior initial-boundary value problem for Maxwell's equations is considered for certain homogeneous boundary conditions and currents which satisfy corresponding compatibility conditions. Under the assumption that a solution exists, it is shown by means of suitable normed spaces that the sequence of discrete solutions obtained from the horizontal line method converges discretely to this solution. A priori estimations are given both for the discrete solutions and the solution of the given problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010109
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  • 5
    Electronic Resource
    Electronic Resource
    Masthead (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010201
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  • 6
    Electronic Resource
    Electronic Resource
    Error estimates for sampling approximation of non-bandlimited functionsThis research was carried out under the DFG „Schwerpunktprogramm Digitale Signalverarbeitung“ (Bu 166/29, 31). (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 127-137 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new proof of the sampling theorem for non-bandlimited signals is presented. It leads to better rates of convergence for the envolved approximation process. Furthermore, the order of convergence is given for an extended class of functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010202
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  • 7
    Electronic Resource
    Electronic Resource
    Hopf-Bifurkation bei Lasern (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 194-213 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The semiclassical equations describing a ring laser show two successive bifurcations, one stationary and one Hopf bifurcation. This phenomenon is analyzed mathematically. The initial value problem for the laser equations and the stability of the stationary solutions are discussed in detail. The transition to ultrashort laser pulses is shown to be a Hopf bifurcation. The direction of the bifurcation is determined for a numerical example. It turns out that it depends on the parameters of the system.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010206
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  • 8
    Electronic Resource
    Electronic Resource
    Masthead (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010301
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  • 9
    Electronic Resource
    Electronic Resource
    On the integral equation method for the plane mixed boundary value problem of the Laplacian (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 265-321 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Although the plane boundary value problem for the Laplacian with given Dirichlet data on one part Γ2 and given Neumann data on the remaining part Γ2 of the boundary is the simplest case of mixed boundary value problems, we present several applications in classical mathematical physics. Using Green's formula the problem is converted into a system of Fredholm integral equations for the yet unknown values of the solution u on Γ2 and the also desired values of the normal derivatie on Γ1. One of these equations has principal part of the second kind, whereas that one of the other is of the first kind. Since any improvement of constructive methods requires higher regularity of u but, on the other hand, grad u possesses singularities at the collision points Γ1 ∩ Γ2 even for C∞ data, u is decomposed into special singular terms and a regular rest. This is incorporated into the integral equations and the modified system is solved in appropriate Sobolev spaces. The solution of the system requires to solve a Fredholm equation of the first kind on the arc Γ2 providing an improvement of regularity for the smooth part of u. Since the integral equations form a strongly elliptic system of pseudodifferential operators, the Galerkin procedure converges. Using regular finite element functions on Γ1 and Γ2 augmented by the special singular functions we obtain optimal order of asymptotic convergence in the norm corresponding to the energy norm of u and also superconvergence as well as high orders in smoother norms if the given data are smooth (and not the solution).
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010302
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  • 10
    Electronic Resource
    Electronic Resource
    On a class of elliptic singular perturbations with applications in population genetics (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 432-441 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: With the maximum principle for differential equations asymptotic estimates are made for a class of linear elliptic singular perturbation problems with resonant turning point behaviour in some of the independent variables. The method is applied to the stationary solution of the Kolmogorov backward equation in population genetics.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010308
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