Vol. 3, No. 1, 2008

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A global collocation method for two-dimensional rectangular domains

Christopher G. Provatidis

Vol. 3 (2008), No. 1, 185–193
Abstract

This paper proposes the use of a global collocation procedure in conjunction with a previously developed functional set suitable for the numerical solution of Poisson’s equation in rectangular domains. We propose to expand the unknown variable in a bivariate series of monomials ${x}^{i}{y}^{j}$ that exist in Pascal’s triangle. We also propose the use of the bivariate Gordon–Coons interpolation, apart from previous intuitive choices of the aforementioned monomials. The theory is sustained by two numerical examples of Dirichlet boundary conditions, in which we find that the approximate solution monotonically converges towards the exact solution.

Keywords
global collocation, Coons interpolation, Poisson's equation