Application of the method of collocation to solve boundary value problems

Ronto, N. I.

doi:10.1007/bf01085363

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“…The use of collocation methods for the solution of partial differential equations (PDE) has become a subject of intensive interest in the past [Lanczos 1938;Ronto 1971;Russell and Shampine 1972;Finlayson 1972;De Boor and Swartz 1973;Diaz 1977;Houstis 1978;Botha and Pinder 1983]. While most research has focused on the local interpolation of a variable, not many works have appeared concerning the global collocation in two-dimensional problems [Frind and Pinder 1979;Hayes 1980;Van Blerk and Botha 1993].…”

Section: Introductionmentioning

confidence: 99%

A global collocation method for two-dimensional rectangular domains

Provatidis

2008

JOMMS

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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.

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