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# Weighted Residual

## MWR for the first- and third-order differential equations

Sat, 2014-02-15 09:03 - Ajit R. JadhavHi all,

In engineering sciences, we usually end up using either the second- or the fourth-order differential equations, and the MWR (the method of weighted residuals) works pretty well for them.

The question is: how about the first- and the third-order differential equations? Why don't we see any applications of MWR for these odd-ordered differential equations? What gives?

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## The Fundamental Physical Bases of the WR Approach (and, Consequently, of FEM) in General

Mon, 2009-02-02 04:54 - Ajit R. JadhavIt has been quite some time (more than 1.5 years) that I had touched upon the topic of the physical bases of FEM in general, and of the general weighted residual (WR) approach in particular, at iMechanica (see here).

The position I then took was that there is no known physical basis at all for the WR approach---despite its loving portrayals in mathematical terms, or its popularity.

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