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  • 1975-1979  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    A note on the iterative solution of recurrence relations (1977)
    Springer
    Numerische Mathematik 27 (1977), S. 165-170 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of Gauss-Seidel iteration schemes suitable for the stable generation of non-dominant solutions of certain third order linear recurrence relations is developed. The algorithms derived have two main advantages over existing algorithms which generally re-formulate the problem as the solution of a system of algebraic equations. Firstly, unlike existing algorithms, the algorithms developed in this paper automatically determine the size of the system to be solved in all cases and secondly they may be extended directly to an important class of nonlinear recurrence relations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396636
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    High order methods for the numerical integration of ordinary differential equations (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 385-409 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary High order implicit integration formulae with a large region of absolute stability are developed for the approximate numerical integration of both stiff and non-stiff systems of ordinary differential equations. The algorithms derived behave essentially like one step methods and are demonstrated by direct application to certain particular examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398507
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    Paper (German National Licenses)
    Fulltext
  • 3
    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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  • 4
    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)
    Fulltext
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