Local Piecewise Polynomial Projection Methods for an ODE which Give High-Order Convergence at Knots

摘要

Local projection methods which yield C(m-1) piecewise polynomials of order m+k as approximate solutions of a boundary value problem for an m(th) 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)