Part II Numerical Mathematics

BIT Numerical Mathematics

, Volume 29, Issue 2, pp 347-355

First online:

On an interpolatory product rule for evaluating Cauchy principal value integrals

  • Philip RabinowitzAffiliated withDepartment of Applied Mathematics & Computer Science, The Weizmann Institute of Science

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Convergence results for interpolatory product rules for evaluating Cauchy principal value integrals of the form f −1 1 v(x)f(x)/x − λ dx wherev is an admissible weight function have been extended to integrals of the form f −1 1 k(x)f(x)/x − λ dx wherek is an arbitrary integrable function subject to certain conditions. Further, whereas the above convergence results were shown when the interpolation points were the Gauss points with respect to some admissible weight functionw, they are now shown to hold when the interpolation points are Radau or Lobatto points with respect tow.

Mathematics Subject Classification