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  • 1
    Electronic Resource
    Electronic Resource
    Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind (1981)
    Springer
    Numerische Mathematik 36 (1981), S. 347-358 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65R20 ; CR: 5.18
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper deals with the question of the attainable order of convergence in the numerical solution of Volterra and Abel integral equations by collocation methods in certain piecewise polynomial spaces and which are based on suitable interpolatory quadrature for the resulting moment integrals. The use of a (nonlinear) variation of constants formula for the representation of the error function in terms of the defect allows for a unified treatment of equations with continuous and weakly singular kernels.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395951
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The iterative correction method for Volterra integral equations (1996)
    Springer
    BIT 36 (1996), S. 221-228 
    Details
    ISSN: 1572-9125
    Keywords: Volterra integral equations ; collocation ; iterative correction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that the (n − 1)-fold application of an iterative correction technique to the iterated collocation solution corresponding to the one-point Gauss collocation solution for a Volterra integral equation of the second kind l6eads to a significant improvement in the precision of these approximations: the resulting rate of (global) convergence is $$\mathcal{O}\left( {h^n } \right)$$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01731980
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    Paper (German National Licenses)
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