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  • Articles: DFG German National Licenses  (2)
  • stability analysis  (2)
  • 65L07  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Diagonally implicit general linear methods for ordinary differential equations (1993)
    Springer
    BIT 33 (1993), S. 452-472 
    Details
    ISSN: 1572-9125
    Keywords: AMS(MOS) ; 65L05 ; 65L07 ; General linear method ; order conditions ; stability analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate some classes of general linear methods withs internal andr external approximations, with stage orderq and orderp, adjacent to the class withs=r=q=p considered by Butcher. We demonstrate that interesting methods exist also ifs+1=r=q, p=q orq+1,s=r+1=q, p=q orq+1, ands=r=q, p=q+1. Examples of such methods are constructed with stability function matching theA-acceptable generalized Padé approximations to the exponential function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01990528
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Construction of two-step Runge-Kutta methods of high order for ordinary differential equations (1998)
    Springer
    Numerical algorithms 18 (1998), S. 51-70 
    Details
    ISSN: 1572-9265
    Keywords: two-step Runge-Kutta methods ; stability analysis ; least squares minimization ; 65L05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The construction of two-step Runge-Kutta methods of order p and stage order q=p with stability polynomial given in advance is described. This polynomial is chosen to have a large interval of absolute stability for explicit methods and to be A-stable and L-stable for implicit methods. After satisfying the order and stage order conditions the remaining free parameters are computed by minimizing the sum of squares of the difference between the stability function of the method and a given polynomial at a sufficiently large number of points in the complex plane.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019157029031
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    Paper (German National Licenses)
    Fulltext
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