Blair Swartz

Collocation at Gaussian Points

Approximations to an isolated solution of an mth order nonlinear ordinary differential equation with m linear side conditions are determined. These approximations are piecewise polynomial functions of order

Piecewise monotone interpolation

m + k

AZTEC: a front tracking code based on Godunov's method

(degree less than

Collocation Approximation to Eigenvalues of an Ordinary Differential Equation: The Principle of the Thing.

m + k

Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations

) possessing

The Construction and Comparison of Finite Difference Analogs of Some Finite Element Schemes

m - 1

Counter Telescope Measurement of Neutron Flux

continuous derivatives. They are determined by collocation, i.e., by the requirement that they satisfy the differential equation at k points in each subinterval, together with the m side conditions. If the solution of the sufficiently smooth differential equation problem has

Collocation approximation to eigenvalues of an ordinary differential equation: numerical illustrations

m + 2k

Compact, implicit difference schemes for a differential equation's side conditions

continuous derivatives and if the collocation points are the zeroes of the kth Legendre polynomial relative to each subinterval, then the global error in these approximations is

A new inequality for symmetric functions

O(| \Delta |^{m + k} )