Linked Questions
54 questions linked to/from Boundary condition with spatial derivative is ignored by NDSolve
3
votes
1
answer
89
views
Piecewise BVP not working on interval for NDSolve [duplicate]
My Mathematica skills aren't the best but this solution isn't making sense considering the boundary value I am supplying.
The leftmost boundary condition, i.e. at $x=0$, $c[t,x]$ should be $1$ for $t\...
- 66.2k
1
vote
1
answer
185
views
5
votes
1
answer
126
views
Understanding NDSolve's implementation of the method of lines
In order to better understand the MethodOfLines flag, I tried comparing the results of NDSolve for a driven heat equation with a ...
- 66.2k
1
vote
0
answers
55
views
Solving PDE for Diffusion Equation (Boundary Condition Issue) [duplicate]
I am trying to solve this partial diffusion equation shown
$$\dfrac{\partial\overset\sim\rho_c}{\partial\overset\sim t}=D_c(\overset\sim r)A\left(\dfrac{\partial^2\overset\sim\rho_c}{\partial\overset\...
- 66.2k
10
votes
1
answer
918
views
Moving B.C.s in heat diffusion model
I came across the paper Solidification dynamics of an impacted drop regarding a heat equations by Thiévenaz et.al and was interested in knowing how they obtained the graphs presented. From what I ...
- 66.2k
8
votes
1
answer
565
views
Droplet of water-alcohol mixture spreading due to evaporation-caused surface tension gradient
I am trying to solve a coupled system of PDEs for 2 functions h[t,r] and c[t,r], with initial conditions of ...
- 39.8k
3
votes
1
answer
290
views
Piecewise causes ndnum warning in NDSolve
Bug introduced in 5.0, persisting through 13.2.
I try to solve the heat transfer equation with boundary condition that depends on time:
...
- 66.2k
6
votes
2
answers
769
views
NDSolve very slow on 2D heat equation
I am trying to solve the 2D heat equation
$$
\begin{cases}
u_{t}-u_{x x}-u_{y y}=f \\
u(0, x, y)=\sin (2 \pi x) \sin (2 \pi y) \\
u(t, 0, y)=0 \\
u(t, x, 1)=0 \\
u_{x}(t, 1, y)=2 \pi e^{-t} \sin (2 \...
- 39.8k
1
vote
1
answer
232
views
How to solve a reaction-diffusion?
I would like to solve a PDE system reaction-diffusion type (2D spatial + 1 temporal) coupled as described below. Another question of this same system was solved here:
System of nonlinear PDE 2D (...
- 39.8k
8
votes
1
answer
722
views
How to solve a system of PDEs with zip condition?
I have a system of PDEs in the following form,
$$\frac{\partial T_1}{\partial t}=\frac{\partial^2 T_1}{\partial x^2},\,\,0<x<S(t)$$
with $T_1(x,0)=-10,\,\,T_1(0,t)=-10,\,\, T_1(S(t),t)=10$, and
...
- 66.2k
5
votes
2
answers
2k
views
Solving systems of partial differential equations with functions of different number of variables
I am trying to solve the following system of two partial differential equations
$\partial_t G(x,y,t) + \partial_x G(x,y,t)+\partial_y G(x,y,t) = -i\left[f(x,t) + f(y,t)\right] $
$\partial_t f(x,t) + ...
- 66.2k
14
votes
1
answer
1k
views
Why does NDSolve fail to solve the PDEs and spit out mconly warning?
I try to solve two coupled PDEs with NDSolve using the following code:
Set two operators:
...
- 66.2k
5
votes
2
answers
2k
views
2d heat conduction equation: Boundary and initial conditions are inconsistent
I have the following code for a 2d heat c equation:
...
- 39.8k
5
votes
1
answer
485
views
Error in Attempting Moving Boundary Fluid System
Recently I was attempting to solve a moving boundary fluid system on mathematica, which I have managed to convert into a coupled PDE-ODE system based on this helpful reference over here.
The equations ...
- 66.2k
4
votes
1
answer
263
views
Solution from NDSolve doesn't conserve a quantity that should be conserved
I am trying to solve Klein-Gordon equation : $$(\frac{\partial^2}{\partial t^2}-\frac{\partial^2}{\partial x^2}+1)\psi(x,t)=0$$
in a new coordinate system where $x\to y=\frac{x}{L(t)}$.
Here is my ...
- 66.2k