The method of weighted residuals and its relation to certain variational principles for the analysis of transport processes

✍ Scribed by B.A. Finlayson; L.E. Scriven

• Publisher: Elsevier Science
• Year: 1965
• Tongue: English
• Weight: 913 KB
• Volume: 20
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(65)80052-5

✦ Synopsis

The approximation scheme entitled method of weighted residuals is extended to systems of differential equations and vector differential equations. The variational principles proposed by ROSEN, CHAMBERS and BIOT for unsteady-state heat transport are all shown to he applications of the method of weighted residuals. The von-K&m&n-Pohlhausen method and the method of moments are also shown to be special cases. The method is illustrated by application to the problem of unsteady heat transfer to a fluid in ideal stagnation flow. APPROXIMATE analytical solutions to partial differential equations are useful when exact analytical solutions are too difficult or impossible to obtain or