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  • 1
    Electronic Resource
    Electronic Resource
    Nordsieck representation of DIMSIMs (1997)
    Springer
    Numerical algorithms 16 (1997), S. 209-230 
    Details
    ISSN: 1572-9265
    Keywords: DIMSIM methods ; Nordsieck representation ; variable step-size ; error accumulation ; error estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A new representation for diagonally implicit multistage integration methods (DIMSIMs) is derived in which the vector of external stages directly approximates the Nordsieck vector. The methods in this formulation are zero-stable for any choice of variable mesh. They are also easy to implement since changing step-size corresponds to a simple rescaling of the vector of external approximations. The paper contains an analysis of local truncation error and of error accumulation in a variable step-size situation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019195215402
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Experiments with a variable-order type 1 DIMSIM code (1999)
    Springer
    Numerical algorithms 22 (1999), S. 237-261 
    Details
    ISSN: 1572-9265
    Keywords: DIMSIM methods ; Nordsieck representation ; local error estimation ; step size and order changing strategy ; 65L05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The issues related to the development of a new code for nonstiff ordinary differential equations are discussed. This code is based on the Nordsieck representation of type 1 DIMSIMs, implemented in a variable-step size variable-order mode. Numerical results demonstrate that the error estimation employed in the code is very reliable and that the step and order changing strategies are very robust. This code outperforms the Matlab ode45 code for moderate and stringent tolerances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019135630307
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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