On a New Approach to the Computational Solution of Partial Differential Equations
Purchase Print Copy
|Add to Cart||Paperback12 pages||$20.00||$16.00 20% Web Discount|
The most versatile and frequently used method for numerically solving partial differential equations is that of approximation by difference equations. While the method has the advantages of conceptual simplicity, wide applicability, and ready suitability for digital computation, it also has the disadvantages of a predilection toward instability and of a frequent requirement for large storage capacity and excessive computing time. This Memorandum describes a modified approach that may be superior in some instances. Considering a particular equation, the usual difference approximation is replaced with a recurrence relation that clearly preserves such properties as boundedness and nonnegativity and that tends to the solution in the limit.
This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.
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.
The RAND Corporation 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.