The Method of Lines Solution of Partial Differential Equations
The Method of Lines Solution of Partial Differential Equations
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In our eReader you can find the full English version of the book. Read The Method of Lines Solution of Partial Differential Equations 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 The Method of Lines Solution of Partial Differential Equations
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0001791688853 using Gear's method in time and fourth order centered differences in space on a 64 point uniform mesh.
-62- Figure 5. 2 is the graph of the PDE solution at various times. The steady state solution is reached at approximately t = 0, 05, It is clear from Figure 5. 2 that the solution varies rapidly in the region near x = 1. Therefore, the coordinate transformation m. Ethod is indicated. The transformation z = X, m >^ 1, stretches the boundary layer region in a neighborhood of x = 1 .... The transformed equation is 1 2 _2 (5. 12) u^ - (mz ) u + m(m-l)z u - n sinh nu t zz z with boundary conditions u(0, t) =, u(l, t) = 1 .
Equation (5. 12) reduces to (5. 11) for m = 1 as it should. The equation v;as solved for n = 10 and m = 1, 2, ... , 30 and in each case the steady state was determined. The table below lists the maximum, deviation of these steady state solutions from the exact solution (5. 10).
m 1 2 3 4 5 7 10 13 15 20 25 30 Maximum Error 0, . 055 0, . 035 0, . 025 0, . 019 0, .
What to read after The Method of Lines Solution of Partial Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by James M Hyman to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
0001791688853 using Gear's method in time and fourth order centered differences in space on a 64 point uniform mesh.
-62- Figure 5. 2 is the graph of the PDE solution at various times. The steady state solution is reached at approximately t = 0, 05, It is clear from Figure 5. 2 that the solution varies rapidly in the region near x = 1. Therefore, the coordinate transformation m. Ethod is indicated. The transformation z = X, m >^ 1, stretches the boundary layer region in a neighborhood of x = 1 .... The transformed equation is 1 2 _2 (5. 12) u^ - (mz ) u + m(m-l)z u - n sinh nu t zz z with boundary conditions u(0, t) =, u(l, t) = 1 .
Equation (5. 12) reduces to (5. 11) for m = 1 as it should. The equation v;as solved for n = 10 and m = 1, 2, ... , 30 and in each case the steady state was determined. The table below lists the maximum, deviation of these steady state solutions from the exact solution (5. 10).
m 1 2 3 4 5 7 10 13 15 20 25 30 Maximum Error 0, . 055 0, . 035 0, . 025 0, . 019 0, .
What to read after The Method of Lines Solution of Partial Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by James M Hyman to read onlineMoreLess
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