Numerical Evaluation of Cauchy Principal Value Integrals with Singular Integrands
نویسنده
چکیده
Convergence results are proved for sequences of interpolatory integration rules for Cauchy principal value integrals of the form -l k(x)(f(x)/(x-X))dx, -1<A<1, -i when f(x) is singular at a point { / À and the singularity is ignored or avoided. /:'
منابع مشابه
TWO LOW-ORDER METHODS FOR THE NUMERICAL EVALUATION OF CAUCHY PRINCIPAL VSlLUE INTEGRALS OF OSCILLATORY KIND
In this paper, we develop two piecewise polynomial methods for the numerical evaluation of Cauchy Principal Value integrals of oscillatory kind. The two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. Two numerical examples are presented to illustrate the two rules developed, The convergence of the two schemes is proved and some error bounds obtai...
متن کاملAnalysis of singular and near-singular integrals by the continuation approach
We present a summary of the Continuation Approach for a broad class of singular and near-singular integrals. Insight is gained into the behaviour of these integrals, and general formulae for integration are obtained using conventional concepts in calculus. Moreover, conditions for boundedness of the singular integrals arise naturally, showing when a strongly singular integral coincides with the...
متن کاملEvaluation of Singular Integrals by Hyperbolic Tangent Based Transformations
We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations...
متن کاملA Sinc-hunter Quadrature Rule for Cauchy Principal Value Integrals
A Sine function approach is used to derive a new Hunter type quadrature rule for the evaluation of Cauchy principal value integrals of certain analytic functions. Integration over a general arc in the complex plane is considered. Special treatment is given to integrals over the interval (-1, 1). It is shown that the quadrature error is of order 0(e~ ), where N is the number of nodes used, and w...
متن کاملTwo general methods for the numerical approximation of multidimensional Cauchy principal value integrals
The numerical approximation of integrals containing strongly singular integrals, in particular Cauchy principal value integrals, is a major issue connected, e.g., to the boundary integral approach for many types of partial differential equations. Whereas the one-dimensional ∗Institut für Angewandte Mathematik, Technische Universität Braunschweig, Pockelsstraße 14, D-38106 Braunschweig, Germany....
متن کامل