**
Convergence of High-order Deterministic Particle Methods
for the Convection-diffusion Equation
**

(R. Cortez)
#### Abstract

A convergence proof of three high-order deterministic particle
methods for the convection-diffusion equation is presented.
The methods are based on discretizations of an integro-differential
equation in which an integral operator approximates the diffusion
operator. The methods differ in the discretization of this operator.
The conditions for convergence imposed on the kernel that defines
the integral operator include moment conditions and a condition on
the kernel's Fourier transform. Explicit formulas for kernels which
satisfy these conditions to arbitrary order are presented.

*Comm. Pure Appl. Math., 50 (1997), pp. 1235-1260.*

**LaTeX Bibliography:**
@article{Cortez1997,
author = {Ricardo Cortez},
title = {Convergence of high-order deterministic particle
methods for the convection-diffusion equation},
journal = {Comm. Pure Appl. Math.},
volume = {50},
number = {L},
year = {1997},
pages = {1235--1260}
}

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