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A Collocation-Galerkin Method for the Two Point Boundary Value Problem Using Continuous Piecewise Polynomial Spaces

Julio Cesar Diaz
SIAM Journal on Numerical Analysis
Vol. 14, No. 5 (Sep., 1977), pp. 844-858
Stable URL: http://www.jstor.org/stable/2156596
Page Count: 15
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A Collocation-Galerkin Method for the Two Point Boundary Value Problem Using Continuous Piecewise Polynomial Spaces
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Abstract

A collocation-Galerkin method for the two point boundary value problem based on continuous piecewise polynomial spaces is defined where the collocation points are the roots of a Jacobi polynomial. An existence and uniqueness theorem is derived by means of a related variational procedure that is defined using a semi-discrete innerproduct. Optimal rates of convergence are established and O(h2r) order of superconvergence at the nodes is obtained. Additional approximations to the solution and its derivatives that obtain O(h2r) order of superconvergence at any point are described.

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