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  • 1
    Electronic Resource
    Electronic Resource
    Integrability, computation and applications (1995)
    Springer
    Acta applicandae mathematicae 39 (1995), S. 5-37 
    Details
    ISSN: 1572-9036
    Keywords: 58F07 ; integrability ; KdV equation ; nonlinear integrable wave functions ; monodromy problems ; automorphic functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The study of integrable systems and the notion of integrability has been re-energized with the discovery that infinite-dimensional systems such as the Korteweg-de Vries equation are integrable. In this paper, the following novel aspects of integrability are described: (i) solutions of Darboux, Brioschi, Halphen-type systems and their relationships to monodromy problems and automorphic functions, (ii) computational chaos in integrable systems, (iii) we explain why we believe that homoclinic structures and homoclinic chaos associated with nonlinear integrable wave problems, will be observed in appropriate laboratory experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00994624
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A moving Petrov-Galerkin method for transport equations (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1321-1336 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A time-dependent transport equation is solved numerically by using a Petrov-Galerkin technique on a time-dependent grid. A piecewise linear trial solution and piecewise Hermite cubic test functions are used. The same method is also applied to a time-independent problem, in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid-generation techniques. Several numerical examples are given.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180905
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  • 3
    Electronic Resource
    Electronic Resource
    Collocation methods and the solution of conduction-convection problems (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 1093-1101 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The upwinded finite element method was introduced for the solution of conduction-convection problems by considering the model problem, u″-Ku′=0, K〉0, subject to the boundary conditions u(0)=1, u(1)=0. In this paper we consider the solution of this problem by the collocation method using piecewise cubic Hermite polynomials and a uniform grid. We consider the collocation points to be arbitrary parameters which enable us to express the collocation points in terms of the upwinding parameter of the upwinded finite element method. Various choices of the collocation points, including values which lead to complete accuracy in the nodal function values as well as the nodal values of the derivatives are discussed. Finally, we discuss the application of these points to slightly more general problems. Numerical results illustrating the behaviour of these points are given.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620170710
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  • 4
    Electronic Resource
    Electronic Resource
    Generalized Petrov-Galerkin methods for the numerical solution of Burgers' equation (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1273-1289 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Generalized Petrov-Galerkin methods are applied in two different ways for the numerical solution of Burgers' equation. In the first place, it is used to produce upwinding in the way described by Mitchell and Griffiths.9,10 The main objective of this paper is in the second place to use it as a moving finite element method. In particular, it is shown that the methods of Miller and co-workers4-6 and Herbst et al.7,8 can be incorporated in the more general approach presented in this paper. Several choices for the test functions are discussed and numerical results are given.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200708
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  • 5
    Electronic Resource
    Electronic Resource
    On upwind collocation methods (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 1 (1985), S. 97-103 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The upwind collocation method is analysed in a way which clearly demonstrates its similarities to other upwind schemes. The dispersion detected by Dougherty and Pinder5 is shown to be of little significance to the quality of the approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630010303
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    Paper (German National Licenses)
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