Library

feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 37 (1981), S. 157-166 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L07 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Consider the systemy′=f(x,y),y(a)=η,x∈[a,b],y∈R n wheref is continuous and Lipschitzian with respect to the second argument. Very often linear multistep variable stepsize variable formula methods (LM VSVFM's) are used to computey k≈y(xk) on the points of the grid:a=x 0〈x1〈x2〈...〈xN=b. The general LM VSVFM is based on formulae of the following type $$y_k = \sum\limits_{i = 1}^{s_k } {\alpha _i (\bar h_k ,sk)y_{k - i} } + \sum\limits_{i = 0}^{s_k } {h_{k - i} \beta _i (\bar h_k ,s_k )f(x_{k - i} ,y_{k - i} )} $$ whereh k=xk−xk−1, $$\bar h_k = (h_k ,h_{k - 1} , \ldots ,h_{k - s_k } )$$ ,s k≦k, k=1(1)N. The coefficients α i and β i depend on the lasts k+1 stepsizes and on the formula used at stepk. Only the zero-stability properties of some special classes of LM VSVFM's (as for example those based on Adams formulae) were investigated in the literature. A class of three-ordinate LM VSVFM's is defined in this paper. Some results concerning the zero-stability properties of these methods are proved. It is shown that some well-known results are simple corollaries of the results found for the three-ordinate LM VSVFM's. It is easily seen that similar results hold for the corresponding one-leg VSVFM's. Finally, the use of the theoretical results in the practical implementations is briefly discussed.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 31 (1978), S. 175-182 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary When variable stepsize variable formula methods (VSVFM's) are used in the solution of systems of first order differential equations instability arises sometimes. Therefore it is important to find VSVFM's whose zerostability properties are not affected by the choice of both the stepsize and the formula. The Adams VSVFM's are such methods. In this work a more general class of methods which contains the Adams VSVFM's is discussed and it is proved that the zero-stability of the class is not affected by the choice of the stepsize and of the formula.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 3
    Electronic Resource
    Electronic Resource
    Bingley : Emerald
    Environmental management and health 10 (1999), S. 216-223 
    ISSN: 0956-6163
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Medicine , Economics
    Notes: Describes a tracer model, DREAM (the Danish Rimpuff and Eulerian Accidental release Model), developed for studying transport, dispersion, and deposition of air pollution caused by a single but strong source. The model is based on a combination of a Lagrangian short-range puff model and a Eulerian long-range transport model. It has been run and validated against measurements from the two European Tracer Experiment (ETEX) releases and from the Chernobyl accident. An air pollution forecast system, THOR, is under development, to make forecasts of various air pollutants on a European scale. Some preliminary results are shown. DREAM will be implemented in THOR for calculations of real time predictions of transport, dispersion and deposition of radioactive material from accidental releases (e.g. Chernobyl). Some applications of the DREAM model and examples of model results are described.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 4
    Electronic Resource
    Electronic Resource
    Springer
    BIT 24 (1984), S. 700-715 
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Systems of ordinary differential equations obtained by using splitting-up techniques in some air pollution models and a pseudospectral (Fourier) discretization of the first-order space derivatives are considered. The application of a fairly general class of predictor-corrector (PC) schemes in the time-discretization process is discussed. Several corrections with different corrector formulae are carried out in thesePC schemes. The classicalDahlquist theory valid for the case when the stepsize is constant is preserved (under very mild restrictions on the stepsize) when suchPC schemes are used as variable stepsize variable formula methods (VSVFM's). This fact is exploited by allowing the stepsize to follow the variation of a certain norm of the wind velocity vector in aVSVFM based on specially constructedPC schemes with large intervals of absolute stability on the imaginary axis. A device that attempts to check both the accuracy and the stability in the course of the integration process has been developed. The code based on the application of thisVSVFM in the time-integration part of the treatment of both 2-dimensional and 3-dimensional models has been tested by using meteorological data prepared at stations located in practically all European countries. The numerical results indicate thatPC schemes with several correctors can successfully be used for the class of problems under consideration. The main reason for this success is the special nature of the computational cost per time-step (due to the splitting approach used). Some short remarks on the possibility of extending the results for large systems ofODE's arising in the treatment of other classes of problems are made.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 5
    ISSN: 1572-9125
    Keywords: Ordinary Differential Equations ; Predictor-Corrector Methods ; Regions of Absolute Stability ; Order and Accuracy ; Numerical Experiments
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two-parameter families of predictor-corrector methods based upon a combination of Adams- and Nyström formulae have been developed. The combinations use correctors of order one higher than that of the predictors. The methods are chosen to give optimal stability properties with respect to a requirement on the form and size of the regions of absolute stability. The optimal methods are listed and their regions of absolute stability are presented. The efficiency of the methods is compared to that of the corresponding Adams methods through numerical results from a variable order, variable stepsize program package.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1051-1061 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of finite element methods to parabolic partial differential equations leads to large linear systems of first-order ordinary differential equations. Very often these systems are stiff and difficulties arise in their numerical solution. We attempt to analyse the problem of how to select numerical methods for the solution of such linear systems.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 7
    Book
    Book
    Boston u.a. :Kluwer,
    Title: Computational methods for general sparse matrices; 65
    Author: Zlatev, Zahari
    Publisher: Boston u.a. :Kluwer,
    Year of publication: 1991
    Series Statement: Mathematics and its applications 65
    Type of Medium: Book
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...