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| Meta Title | Solve Nonlinear 2nd Order Partial Differential Equation Numerically? - Online Technical Discussion Groups—Wolfram Community |
| Meta Description | Wolfram Community forum discussion about Solve Nonlinear 2nd Order Partial Differential Equation Numerically?. Stay on top of important topics and build connections by joining Wolfram Community groups relevant to your interests. |
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| Boilerpipe Text | Hey!
I am kind of new to mathematica so I don't know a lot of stuff...
So trying to put the question in context... I want to know if there is a way in Mathematica 9 to solve
Nonlinear Second Order Parial Differential Equation?
I understand that I cannot use
DSolve
since its a Second Order PDE but even with
NDSolve
, I keep getting errors..
My
PDEs
are something like this:
fpde = (1 + (D[y[x, t], t])^2) (D[y[x, t], {x, 2}]) + (1 + (D[y[x, t], x])^2) (D[y[x, t], {t, 2}]) == 0;
i.e.
(1 + (
d
y /
d
t)^2 ) * (
d2
y /
d
x2)) + (1 + (
d
y /
d
x)^2 ) * (
d2
y /
d?
t2)) = 0
where y is a function of x and t.
I also give
two boundary conditions
and
one initial conditon
while using NDSolve
I have tried the following:
mysol = NDSolve[{fpde, y[0, t] == 0, y[2 Pi, t] == 0, y[x, Pi/4] == 0}, y, {x, 0, 2 Pi}, {t, 0, 2 Pi}]
Error : The number of constraints (1) (initial conditions) is not equal to the total differential order of the system plus the number of discrete variables (2).
mysol = NDSolve[{fpde, y[0, t] == 0, y[2 Pi, t] == 0, Derivative[1, 0][y][x, 2 Pi] == Tan[x]}, y, {x, 0, 2 Pi}, {t, 0, 2 Pi}]
Error: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable.
I can't figure out if my application of the command is incorrect or if a different approach is required to solve such PDEs.
My objective is to get the numerical solution to such an equation.
Thanks a lot! |
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| Readable Markdown | null |
| Shard | 184 (laksa) |
| Root Hash | 3744487911316863784 |
| Unparsed URL | com,wolfram!community,/groups/-/m/t/149586 s443 |