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Feb
3
awarded  Popular Question
Feb
3
comment Phase Portrait to Differential Equation
Curious to know why this received a "close" request?
Feb
3
asked Phase Portrait to Differential Equation
Feb
3
awarded  Nice Question
Jan
30
comment How can I solve a 3D heat transfer partial differential equation?
Try looking up NDSolve and NDSolveValue. They both demonstrate the heat equation in (x,y,t). You should be able to extend that to (x,y,z,t). Two-Dim code.
Jan
25
awarded  Yearling
Jan
16
comment Heat convection differential equations from 1952 - Mathematica “fails to converge”
@xzczd Could you share a link (if on SE, i.e) to the issue you were having with the Young-Laplace equation? I would be interested to look at it. I am into analytical fluid dynamics and heat transfer and mathematica has revolutionized it for me!
Jan
16
comment How do I solve a PDE with a strange boundary condition?
@xzczdYou worked this problem from a robust fundamental theory put forth by Boris Galerkin!! Bad news for the folks at mathematica ;).. for you'll put them out of business ;)!!! With your permission, I would like to demonstrate your answer to my undergraduate class (that I teach) on FEM.
Jan
16
comment Heat convection differential equations from 1952 - Mathematica “fails to converge”
@xzczd Yes, this (both F and H) will be asymptotic in the far field. I found a mathematica file that uses the Shooting method by expressing one of these coupled variables as an initial condition. Alas, I do not have the time to express this here because of a lack of time today! I'll try to get to it in the evening.
Jan
15
comment Heat convection differential equations from 1952 - Mathematica “fails to converge”
I just found this. I'll experiment with this and add more detail to this problem.
Jan
15
asked Heat convection differential equations from 1952 - Mathematica “fails to converge”
Dec
17
awarded  Good Question
Nov
26
awarded  Notable Question
Nov
13
comment Solution of Poisson equation with two regions
Can this be a case for "matched asymptotics" (perturbation methods)?.. or am I over-complicating the problem?
Oct
31
comment Shooting Method in Mathematica
I am curious to know what physics this is capturing. Looks like Falkner-Skan... boundary layer phenomenon? Have you tried NDSolve. I realize this isn't what you may have asked but as a lover of NDSolve... I just had to suggest that.
Oct
27
awarded  Popular Question
Oct
5
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
As mentioned, I am posting my comment about this answer and the question. The question itself, for those who are familiar with solid mechanics, is a fundamental problem in solid mechanics. The answer here allows me to juxtapose the time-evolution behavior of an annular plate with that obtained from menu/GUI driven commercial FEA solvers. It turns out that, yet again, for fundamental problems in mechanics (solid/fluid), Mathematica outdoes what other commercial solvers would do. The main problem I was trying to solve was the deflection of an orifice plate (4th order biharmonic eqn).
Sep
26
awarded  Benefactor
Sep
26
comment Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
Thank you for both your detailed answers. I will post a detailed comment soon. I love the analytical solution, personally!
Sep
26
accepted Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)