6533b856fe1ef96bd12b2f39

RESEARCH PRODUCT

Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialf�llen

Claus Schneider

subject

Computational MathematicsLogarithmApplied MathematicsNumerical analysisMathematical analysisGravitational singularityFinite algorithmAlgebraic numberMathematicsNumerical integrationQuadrature (mathematics)

description

Recursions are given for Richardson-extrapolation based on generalized asymptotic expansions for the solution of a finite algorithm depending upon a parameterh>0. In particular, these expansions may contain terms likeh ?·log(h), (?>0). Simplified formulae are established in special cases. They are applicable to numerical integration of functions with algebraic or logarithmic endpoint singularities and provide a Romberg-type quadrature.

https://doi.org/10.1007/bf01400966