Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels

Authors:
Sheon-Young Kang;Israel Koltracht;George Rawitscher
Affiliations:
Department of Mathematics, Purdue University North Central, Westville, Indiana;Department of Mathematics, University of Connecticut, Storrs, Connecticut;Department of Physics, University of Connecticut, Storrs, Connecticut
Venue:
Mathematics of Computation
Year:
2003

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Abstract

A new highly accurate numerical approximation scheme based on a Gauss type Clenshaw-Curtis quadrature for Fredholm integral equations of the second kind x(t) + ∫ab k(t, s)x(s)ds = y(t), whose kernel k(t,s) is either discontinuous or not smooth along the main diagonal, is presented. This scheme is of spectral accuracy when k(t,s) is infinitely differentiable away from the diagonal t = s. Relation to the singular value decomposition is indicated. Application to integro-differential Schrödinger equations with nonlocal potentials is given.