The Convergence of Even Degree Spline Collocation Solution for Potential Problems in Smooth Domains of the Plane.
J. Saranen (1988)
Numerische Mathematik
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Displaying similar documents to “Spline Collocation for Singular Integro-differential Equations over (0, 1).”
The Convergence of Even Degree Spline Collocation Solution for Potential Problems in Smooth Domains of the Plane.
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We prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials. ...