Cover: On Nonlinear Differential Equations, the Maximum Operation, and Monotone Convergence

On Nonlinear Differential Equations, the Maximum Operation, and Monotone Convergence

Published 1957

by Robert E. Kalaba

Download

Download eBook for Free

FormatFile SizeNotes
PDF file 2.6 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

Purchase

Purchase Print Copy

 Format Price
Add to Cart Paperback98 pages $30.00

A proof that the solutions to certain classes of nonlinear ordinary and partial differential equations may be represented in terms of the maximum operation applied to the solutions of associated linear equations. This, in effect, affords a new approach to the quasi-linearization of nonlinear differential equations. The representation readily yields uniform lower bounds for solutions, and, in the case of stochastic nonlinear differential equations, leads to representations for the distribution functions of the solutions. In addition, a technique is provided for constructing monotone sequences of functions which converge quadratically to the solution of the nonlinear equation, which is of value in machine computation.

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.