A CHEBYSHEV POLYNOMIAL
COLLOCATION BIEM FOR MIXED
BOUNDARY VALUE PROBLEMS
ON NONSMOOTH BOUNDARIES

L. SCUDERI

Abstract:

We propose a Chebyshev polynomial collocation method to solve systems of boundary integral equations arising from a BIE formulation of the mixed Dirichlet-Neumann boundary value problem for the Laplace equation on a nonsmooth domain. In particular, we first improve the behavior of the solution near the corners by introducing a smoothing transformation and then we apply to the new system a collocation method using Chebyshev polynomial expansions as approximants and the zeros of Chebyshev polynomials as collocation nodes. We give a complete solvability and stability analysis of the transformed integral equations by using localization and Mellin techniques. The numerical results obtained show the efficiency of the method here proposed.