Reprint Server

From Taylor Series to Taylor Models

Abstract

An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on the set of Taylor models, arbitrary order integrators with rigorous remainder treatment are developed. The integrators can meet pre-specified accuracy requirements in a mathematically strict way, and are a stepping stone towards fully rigorous estimates of stability of repetitive systems.

M. Berz, Chapter in: "Nonlinear Problems in Accelerator Physics" (1997) 1-27, American Institute of Physics CP405

Download

Click on the icon to download the corresponding file.

Download Postscript version (389529 Bytes).
Download Adobe PDF version (221427 Bytes).

Go Back to the reprint server.
Go Back to the home page.

This page is maintained by Kyoko Makino. Please contact her if there are any problems with it.