DOIAbstract
AbstractInterpolatory integration rules of numerical stability are presented for approximating Cauchy principal value (p.v.) integrals ⨍−11f(t)/(t−c)dt and Hadamard finite part (f.p.) integrals ∫=−11f(t)/(t−c)2dt, −1<c<1, respectively, for a given smooth function f(t). Present quadrature rules consist of interpolating f(t) at abscissae in the interval of integration [−1,1] except for the pole c, where neither the function value f(c) nor its derivative f′(c) is required, followed by subtracting out the singularities.We demonstrate that the use of both endpoints ±1 as abscissae in interpolating f(t) is essential for uniformly approximating the integrals, namely for bounding the approximation errors independently of the values of c. In fact, f...
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