On the convergence of the method for indefinite integration of oscillatory and singular functions
P Keller, P Woźny - Applied mathematics and computation, 2010 - Elsevier
P Keller, P Woźny
Applied mathematics and computation, 2010•ElsevierWe consider the problem of convergence and error estimation of the method for computing
indefinite integrals proposed in Keller [8]. To this end, we have analysed the properties of
the difference operator related to the difference equation for the Chebyshev coefficients of a
function that satisfies a given linear differential equation with polynomial coefficients.
Properties of this operator were never investigated before. The obtained results lead us to
the conclusion that the studied method is always convergent. We also give a rigorous proof …
indefinite integrals proposed in Keller [8]. To this end, we have analysed the properties of
the difference operator related to the difference equation for the Chebyshev coefficients of a
function that satisfies a given linear differential equation with polynomial coefficients.
Properties of this operator were never investigated before. The obtained results lead us to
the conclusion that the studied method is always convergent. We also give a rigorous proof …
We consider the problem of convergence and error estimation of the method for computing indefinite integrals proposed in Keller [8]. To this end, we have analysed the properties of the difference operator related to the difference equation for the Chebyshev coefficients of a function that satisfies a given linear differential equation with polynomial coefficients. Properties of this operator were never investigated before. The obtained results lead us to the conclusion that the studied method is always convergent. We also give a rigorous proof of the error estimates.
Elsevier
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