Accession Number:

ADA089589

Title:

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

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

• DE Boor,Carl
• Swartz,Blair

Report Date:

1980-05-01

Pagination or Media Count:

22.0

Abstract:

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

Descriptors:

• *BOUNDARY VALUE PROBLEMS
• *CONVERGENCE
• MATRICES(MATHEMATICS)
• EIGENVALUES
• POLYNOMIALS
• LEAST SQUARES METHOD
• THEOREMS

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE