Local Piecewise Polynomial Projection Methods for an ODE which Give High-Order Convergence at Knots.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Local projection methods which yield Cm-1 piecewise polynomials of order mk as approximate solutions of a boundary value problem for an mth order ordinary differential equation are determined by the k linear functionals at which the residual error in each partition interval is required to vanish. We develop a condition on these k functionals which implies breakpoint superconvergence of derivatives of order less than m for the approximating piecewise polynomials. The same order of super-convergence is associated with eigenvalue problems. Author
- Statistics and Probability