Some Remarks Concerning the Bremmer Series
Some Remarks Concerning the Bremmer Series
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In our eReader you can find the full English version of the book. Read Some Remarks Concerning the Bremmer Series 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 Some Remarks Concerning the Bremmer Series
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After the substitution u(x) = K(x)v(x) there results in place of (i|-. L) the differential equation v'(x) = [-K"-'-(x)K'(x) + k"^(x)A(x)k(x)]v(x) . {h. 2) The solution given in this section is due to Keller and Keller.
p] 11 - The differential equation (i4-. 2) is a generalization of the system (2. 10-11).
Let the diagonal elements of the matrix k' (x)K'(x) be 7 (x) . Then define the matrix Y(x) as the solution of the differential equation Y'(x) = [-r(x) + K-^(x)A(x)K(x)]Y(x), (U. 3) where r(x)... is the diagonal part of k" (x)K'(x). The matrix Y(x) is diagonal and can be calculated explicitly since the matrix factor of Y(x) on the right of (4. 3) is diagonal. The solution Y(x) is determined except for an arbitrary constant diagonal matrix factor which can be taken to be the identity. The n-th diagonal element of Y(x) will have the form Y (x) = exp n X / 7^(s)ds + / K^(s) ds ■- o (h. K) Now define the vector p(x) by v(x) = Y(x)p(x) and substitute into (i
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To quickly assess the difficulty of the text, read a short excerpt:
After the substitution u(x) = K(x)v(x) there results in place of (i|-. L) the differential equation v'(x) = [-K"-'-(x)K'(x) + k"^(x)A(x)k(x)]v(x) . {h. 2) The solution given in this section is due to Keller and Keller.
p] 11 - The differential equation (i4-. 2) is a generalization of the system (2. 10-11).
Let the diagonal elements of the matrix k' (x)K'(x) be 7 (x) . Then define the matrix Y(x) as the solution of the differential equation Y'(x) = [-r(x) + K-^(x)A(x)K(x)]Y(x), (U. 3) where r(x)... is the diagonal part of k" (x)K'(x). The matrix Y(x) is diagonal and can be calculated explicitly since the matrix factor of Y(x) on the right of (4. 3) is diagonal. The solution Y(x) is determined except for an arbitrary constant diagonal matrix factor which can be taken to be the identity. The n-th diagonal element of Y(x) will have the form Y (x) = exp n X / 7^(s)ds + / K^(s) ds ■- o (h. K) Now define the vector p(x) by v(x) = Y(x)p(x) and substitute into (i
What to read after Some Remarks Concerning the Bremmer Series?
You can find similar books in the "Read Also" column, or choose other free books by Irvin W Kay to read onlineMoreLess
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