All micmac ! How come things disappear so quick ?
but in reference to the "Galerkin MC.mcd" that has appeared these days.
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I have reviewed the work sheet, not about the construct of the DE, rather about your lsolve[matrix(3),-f(3)]. "lsove", solves in the least square sense, therefore uniquely in Lagrange polynomial format (as you have). In Mathcad there is a more general and more powerful solve "linfit".
"linfit" solves for a vector of model functions. In this case, and looking at the allure of the Odesolve, we chose Cheby but we could chose any other ortho poly or even a user vector of model functions, v.g: some rational terms. Understanding all these is very subtile. Cheby fits a much wider class of curves than purely Lagrange, thus the choice in collocation. On that point, the best example is trying to fit ln(x) by only the native Lagrange, like in regress(Mx, vy, n) ... that fit is impossible for high accuracy. The deluxe ln(x) is Cheby.
That a Cheby re-expands in Lagrange form is a fact, but that was not my point... rather to arrive at the final approximation. This work sheet is completely automated, changing components in the Odesolve (as long as valid), the last formula for export will update. You will just have to press F9 on READPRN to update the coefficients.
Enjoy, this work sheet is for the box.
jmG
PS: I will conserve this work sheet, but would appreciate to credit the parts of it ... who should I cedit the original "Galerkin MC.mcd" ??? This morning, I couldn't retrace that sheet to any poster has it seems to have vaporized in the blue.
