Smoothness is a desirable characteristic of interpolated zero curves; not only is it intuitively appealing, but there is some evidence that it provides more accurate pricing of securities. This paper outlines the mathematics necessary to understand the smooth interpolation of zero curves, and describes two useful methods: cubic-spline interpolation—which guarantees the smoothest interpolation o...

We describe the use of upwind monotonic interpolation methods for the solution of the time-dependent radiative transfer equation in both optically thin and thick media. These methods, originally developed to solve Eulerian advection problems in hydrodynamics, have the ability to propagate sharp features in the ow with very little numerical di usion. We consider the implementation of both explic...

A simple and explicit method is given for approximating the unit ball of `p by polytopes. The method leads to a natural generalization of `p-spaces with good duality and interpolation properties.

Abstract. Interests in meshfree (or meshless) methods have grown rapidly in the recent years in solving boundary value problems arising in mechanics, especially in dealing with difficult problems involving large deformation, moving discontinuities, etc. Rigorous error estimates of a meshfree method, the reproducing kernel particle method (RKPM), have been theoretically derived and experimentall...

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H(Ω) (k ≥ 1). With a special kind of radial basis function, we construct a basis in H(Ω) and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density. Mathematics subject classification: 41...

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstiff initial value problems were given in [D. This work describes an alternative approach based on Hermite-Birkhoff interpolation. The new approach has two main advantagesmit is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. F...

Xinjie Wang,1 Jonathan R. Yates,2,3 Ivo Souza,2,3 and David Vanderbilt1 1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA 2Department of Physics, University of California, Berkeley, California 94720, USA 3Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Received 10 August 2006; published 21 November...

An explicit method is derived for collocating either of the convolution integrals p(x) = fi f(x t)g(t)dt or q(x) = /*/(< x)g(t)dt, where x 6 (a, b), a subinterval of M . The collocation formulas take the form p = F(Am)% or q = F(Bm)g, where g is an w-vector of values of the function g evaluated at the "Sine points", Am and Bm are explicitly described square matrices of order m, and F(s) = ¡Qexp...

The solution of time-dependent partial diierential equations with discrete time static remesh-ing is considered within a method of lines framework. Numerical examples in one and two space dimensions are used to show that spatial interpolation error may have an important impact on the eeciency of integration. Analysis of a simple problem and of the time integration method is used to connrm the e...