A Critique of the Variational Method in Scattering Problems
A Critique of the Variational Method in Scattering Problems
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In our eReader you can find the full English version of the book. Read A Critique of the Variational Method in Scattering Problems Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Critique of the Variational Method in Scattering Problems
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Is used, the set is also required to be complete. Now try an approximation G to g given by (8) G . N c^G^ n where the sum may involve either a finite or infinite number of terms and the constants c are to determined. We shall now prove the following - 5 - Theorem 1 The necessary and sufficient conditions for the express- ion in (7) to be stationary for small variations of G are (9) (^» V ' (°n' ^^ (n-0, 1, ... ).
G then satisfies (f, G) = (G, LG) and A - (f, G).
The importance of this theorem l...ies in the fact that equations (9) are precisely those obtained by substituting the expansion (8) in (1) and taking the inner product of both sides with G, which is Galerkin's process.
Then A may be calculated directly from its original definition (2) because the approximation satisfies the reciprocity theorem. Obviously this direct method of setting up the equations is to be preferred to determining them via the variation principle. It should be remarked that, if we make a one -terra approximation so that G » c G, the reciprocity theorem is satisfied if 00 (f, G^) « c^(G^, LG^) and (f, G) becomes (f, Gq)^/(Gq, UG ) which is the same as would be calculated from (7).
What to read after A Critique of the Variational Method in Scattering Problems?
You can find similar books in the "Read Also" column, or choose other free books by D S Jones to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Is used, the set is also required to be complete. Now try an approximation G to g given by (8) G . N c^G^ n where the sum may involve either a finite or infinite number of terms and the constants c are to determined. We shall now prove the following - 5 - Theorem 1 The necessary and sufficient conditions for the express- ion in (7) to be stationary for small variations of G are (9) (^» V ' (°n' ^^ (n-0, 1, ... ).
G then satisfies (f, G) = (G, LG) and A - (f, G).
The importance of this theorem l...ies in the fact that equations (9) are precisely those obtained by substituting the expansion (8) in (1) and taking the inner product of both sides with G, which is Galerkin's process.
Then A may be calculated directly from its original definition (2) because the approximation satisfies the reciprocity theorem. Obviously this direct method of setting up the equations is to be preferred to determining them via the variation principle. It should be remarked that, if we make a one -terra approximation so that G » c G, the reciprocity theorem is satisfied if 00 (f, G^) « c^(G^, LG^) and (f, G) becomes (f, Gq)^/(Gq, UG ) which is the same as would be calculated from (7).
What to read after A Critique of the Variational Method in Scattering Problems?
You can find similar books in the "Read Also" column, or choose other free books by D S Jones to read onlineMoreLess
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