Abstract
In this paper we study the numerical computation of Stieltjes integrals using numerical quadrature and numerical differentiation. It is shown how this may be done in a stable way. Asymptotic expansions for the discretization error will be given. A similar approach will enhance the stability of the numerical computation of integrals containing higher order derivatives.
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References
Lyness, J.N. (1968) The Calculation of Stieltjes Integral. Numer. Math. 12, 252–265.
van der Sluls, A. (1972) The remainder term in quadrature formulae. Numer. Math. 19, 49–55.
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© 1988 Springer Basel AG
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van der Sluis, A. (1988). Stable Computation of Stieltjes Integrals. In: Braß, H., Hämmerlin, G. (eds) Numerical Integration III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 85. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6398-8_24
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DOI: https://doi.org/10.1007/978-3-0348-6398-8_24
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2205-2
Online ISBN: 978-3-0348-6398-8
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