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Finite Difference Methods for PDEs

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See the attached file.
B. A beam is resting horizontally on the sharp edges of a room with width L, and has a ceiling attached in the shape ....
At time t = 0 the glue releases and the beam
vibrates. Describe the vibration for t > 0 if the situation is described by
...
Boundary and initial values are given by
.....
Hint: Use separation of variables so that .....and choose the coordinates so
....
that x = 0 at height H.
Any Handbook on Mathematics for Engineers can be consulted.

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Finite difference methods for PDEs are investigated and found in the solution. The solution is detailed and well presented.

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Improved Euler method with Butcher Tableau

Use the order conditions to prove that the improved Euler method with Butcher Tableau

0 |
1 | 1
---+-------------
| 1/2 1/2

is second order but not third order.

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