Galerkins method starts with the differential equation (say u 00 = f(x)) instead of the
Chapter 6, Problem 6.5.5(choose chapter or problem)
Galerkins method starts with the differential equation (say u 00 = f(x)) instead of the energy P. The trial solution is still u = y1V1 +y2V2 ++ynVn, and the ys are chosen to make the difference between u 00 and f orthogonal to every Vj : Galerkin Z (y1V 00 1 y2V 00 2 ynV 00 n )Vjdx = Z f(x)Vj(x)dx. integrate the left side by parts to reach Ay = f , proving that Galerkin gives the same A and f as Rayleigh-Ritz for symmetric problems.
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