Some Implicit Finite Difference Schemes for Hyperbolic Systems
Some Implicit Finite Difference Schemes for Hyperbolic Systems
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In our eReader you can find the full English version of the book. Read Some Implicit Finite Difference Schemes for Hyperbolic Systems 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 Implicit Finite Difference Schemes for Hyperbolic Systems
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] = 0. From this we have [i3Ax. ], =a. (l-^a, ). Therefore || x || - || x || = -a or a < 0. This in turn 3 k J kK jTi J J J t^*^ yields the convergence of ||x. || which shows that a. — 0. Since r3Ax 1 = «. (1 -^a, , ) we can prove that x. — 0. J k J kk J If the matrix A is given by equations (2. 1) we are no longer able to obtain a stability condition by analytic means. However we can compute the eigenvalues of the amplification matrix numerically and thus determine a stability condition. The difference equation is n+1 n . . / n. N+1 .^ . , n n w = w - At A^ (w ) w/v - At A_, (w ) wa . L X U X If A(w) is defined by equations (2. 1), then the amplification matrix for this scheme is - 12 - 2. 0 1. 5 1. 0 Figure 1. Stability of the Q-C-N scheme (uncentered) 13 2 I K cvi - 14 R = 1 1 + ia 1 1 + iof - iff pd+ior)' i/3p 1 + la jffTP 1 + ice - ff 7p Pd+iof)' 1 + iof where /3 = (At sin u Ax) /Ax and or - /3u. The eigenvalues of R are given by H . /(I +ia) where ^„ = 1 and p . (j = 1, 2) are the roots of the following quadratic - (2-6)^ + 1 = 6 = r2 2 P c 1 + ior Note that the eigenvalues of R depend only on a = /3c and M = u/c.
What to read after Some Implicit Finite Difference Schemes for Hyperbolic Systems?
You can find similar books in the "Read Also" column, or choose other free books by John Gary to read online
To quickly assess the difficulty of the text, read a short excerpt:
] = 0. From this we have [i3Ax. ], =a. (l-^a, ). Therefore || x || - || x || = -a or a < 0. This in turn 3 k J kK jTi J J J t^*^ yields the convergence of ||x. || which shows that a. — 0. Since r3Ax 1 = «. (1 -^a, , ) we can prove that x. — 0. J k J kk J If the matrix A is given by equations (2. 1) we are no longer able to obtain a stability condition by analytic means. However we can compute the eigenvalues of the amplification matrix numerically and thus determine a stability condition. The difference equation is n+1 n . . / n. N+1 .^ . , n n w = w - At A^ (w ) w/v - At A_, (w ) wa . L X U X If A(w) is defined by equations (2. 1), then the amplification matrix for this scheme is - 12 - 2. 0 1. 5 1. 0 Figure 1. Stability of the Q-C-N scheme (uncentered) 13 2 I K cvi - 14 R = 1 1 + ia 1 1 + iof - iff pd+ior)' i/3p 1 + la jffTP 1 + ice - ff 7p Pd+iof)' 1 + iof where /3 = (At sin u Ax) /Ax and or - /3u. The eigenvalues of R are given by H . /(I +ia) where ^„ = 1 and p . (j = 1, 2) are the roots of the following quadratic - (2-6)^ + 1 = 6 = r2 2 P c 1 + ior Note that the eigenvalues of R depend only on a = /3c and M = u/c.
What to read after Some Implicit Finite Difference Schemes for Hyperbolic Systems?
You can find similar books in the "Read Also" column, or choose other free books by John Gary to read online
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