Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Numerical Approximations to Hadamard Finite-part Integral Operators

by
Prof. Weiwei Sun
Department of Mathematics
City University of Hong Kong

Date: March 28, 2007 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: Many physical problems require efficient discrete schemes for Hadamard finite-part integral operators and efficient quadrature rules for the evaluation of such integrals in the form



where s∈(a, b) is the singular point.
               In this talk, we present a general framework of interpolative quadrature rules for the Hadamard finite-part integral. The Gaussian quadrature rules and Newton-Cotes formulas are viewed as special cases. We establish the pointwise superconvergence phenomenon of these interpolative quadrature rules, that is, when the singular point coincides with certain a priori known points, the accuracy is better than what is globally possible. A new quadrature rule of Gaussian type is proposed for the evaluation of integrals simultaneously with different types of singularities. Several collocation-type approximations to Hadamard integral operators are presented. These discrete approximations are of Toeplitz or nearly Toeplitz structure, which gives many advantages in developing fast linear solvers for numerical solution of intego-differential equations.

             

** All interested are welcome **

For enquiry: 2788-9816

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