Timeline for Conservation of area solving a PDE via finite difference scheme
Current License: CC BY-SA 3.0
9 events
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| Jun 7, 2017 at 15:01 | vote | accept | mch56 | ||
| Apr 13, 2017 at 12:55 | history | edited | CommunityBot |
replaced http://mathematica.stackexchange.com/ with https://mathematica.stackexchange.com/
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| Dec 16, 2016 at 10:45 | comment | added | mch56 | yes, this is intentional, purely due to the physics under consideration during the derivation of equation 1 and equation 2. That was one mistake I had made. Thanks for editing your answer with a full solution for equation 1. It is much much faster than my version. | |
| Dec 16, 2016 at 9:56 | vote | accept | mch56 | ||
| Dec 16, 2016 at 10:41 | |||||
| Dec 14, 2016 at 19:00 | history | edited | bbgodfrey | CC BY-SA 3.0 |
added Eq 1 results
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| Dec 14, 2016 at 17:31 | comment | added | bbgodfrey |
@ojlm Try D[u[i, t], t] == ((up^3 (1 - up)^3) (ϵ dup Cos[L + (i - 1/2) d] - (1 + ϵ up) Sin[L + (i - 1/2) d]) - (um^3 (1 - um)^3) (ϵ dum Cos[L + (i - 3/2) d] - (1 + ϵ um) Sin[L + (i - 3/2) d]))/d (with your definition of h0).
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| Dec 14, 2016 at 16:12 | comment | added | bbgodfrey |
@ojlm Your z0 and h0 are defined differently. Consequently, Eq 2 with initial and boundary conditions is not the same as the limit of Eq 1 with initial and boundary conditions for small θ. Is this intentional?
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| Dec 14, 2016 at 11:11 | comment | added | mch56 |
Thanks for the reply. So if I understand correctly, you have not differentiated equation 2 before discretising. Suppose now I wished to discretise equation 1 in the same manner, my attempt is as follows (as per your answer 129183) D[u[i, t], t] == (up^3 (1 - up)^3 ((1 + \[Epsilon]*up) Sin[(i - 1) d] - \[Epsilon]* Cos[(i - 1) d] dup) - um^3 (1 - um)^3 ((1 + \[Epsilon]*um) Sin[(i - 1) d] - \[Epsilon]* Cos[(i - 1) d] dum)) /d However this does not work. I presume a problem with the $\sin \theta$ and $\cos \theta$ terms?
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| Dec 12, 2016 at 2:30 | history | answered | bbgodfrey | CC BY-SA 3.0 |