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  • 11
    Electronic Resource
    Electronic Resource
    A block method for the numerical integration of stiff systems of ordinary differential equations (1979)
    Springer
    BIT 19 (1979), S. 429-447 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach to the approximate numerical integration of stiff systems of first order ordinary differential equations is developed. In this approach several different formulae are applied in a well defined cyclic order to produce highly accurate integration schemes with infinite regions of absolute stability. The efficiency of these new algorithms, compared with that of certain existing ones, is demonstrated for some particular test problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01931259
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    Paper (German National Licenses)
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  • 12
    Electronic Resource
    Electronic Resource
    A note on the exponential fitting of blended, extended linear multistep methods (1981)
    Springer
    BIT 21 (1981), S. 450-454 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of exponentially fitted blended, extended linear multistep methods is investigated andA-stable formulae of order 3, 4 and 5 are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932841
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    Paper (German National Licenses)
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  • 13
    Electronic Resource
    Electronic Resource
    On a class of cyclic methods for the numerical integration of stiff systems of O.D.E.s (1977)
    Springer
    BIT 17 (1977), S. 270-280 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of cyclic linear multistep methods suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is developed. Particular attention is paid to the problem of deriving schemes which are almostA-stable, self starting, have relatively high orders of accuracy and contain a built in error estimate. These requirements demand that the linear multistep methods which are used are solved iteratively rather than directly in the usual way and an efficient method for doing this is suggested. Finally the algorithms are illustrated by application to a particular test problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932147
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    Paper (German National Licenses)
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  • 14
    Electronic Resource
    Electronic Resource
    A high order method for the numerical solution of two-point boundary value problems (1980)
    Springer
    BIT 20 (1980), S. 44-52 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A one step finite difference scheme of order 4 for the numerical solution of the general two-point boundary value problemy′=f(t,y),a ≦t ≦b, withg(y(a),y(b))=0 is presented. The global discretization error of the scheme is shown, in sufficiently smooth cases, to have an asymptotic expansion containing even powers of the mesh size only. This justifies the use of Richardson extrapolation (or deferred correction) to obtain high orders of accuracy. A theoretical examination of the new scheme for large systems of equations shows that for a given mesh size it generally requires about twice as much work as the Keller box scheme. However, the expectation of higher accuracy usually justifies this extra computational effort. Some numerical results are given which confirm these expectations and show that the new scheme can be generally competitive with the box scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933584
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    Paper (German National Licenses)
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  • 15
    Electronic Resource
    Electronic Resource
    EfficientP-stable methods for periodic initial value problems (1984)
    Springer
    BIT 24 (1984), S. 248-252 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Efficient families ofP-stable formulae are developed for the numerical integration of periodic initial value problems where the required solution has an unknown period. Formulae of orders 4 and 6 requiring respectively 2 and 4 function evaluations per step are derived and some numerical results are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01937491
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    Paper (German National Licenses)
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  • 16
    Electronic Resource
    Electronic Resource
    High order methods for the numerical solution of two-point boundary value problems (1982)
    Springer
    BIT 22 (1982), S. 183-199 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a recent paper, Cash and Moore have given a fourth order formula for the approximate numerical integration of two-point boundary value problems in O.D.E.s. The formula presented was in effect a “one-off” formula in that it was obtained using a trial and error approach. The purpose of the present paper is to describe a unified approach to the derivation of high order formulae for the numerical integration of two-point boundary value problems. It is shown that the formula derived by Cash and Moore fits naturally into this framework and some new formulae of orders 4, 6 and 8 are derived using this approach. A numerical comparison with certain existing finite difference methods is made and this comparison indicates the efficiency of the high order methods for problems having a suitably smooth solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01944476
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  • 17
    Electronic Resource
    Electronic Resource
    Ciliated pits of Stenostoma (1915)
    New York, NY : Wiley-Blackwell
    Journal of Morphology 26 (1915), S. 235-245 
    Details
    ISSN: 0362-2525
    Keywords: Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Medicine
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jmor.1050260204
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    Paper (German National Licenses)
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