All Questions
Tagged with mathematica partial-differential-equations
21
questions
-2
votes
0
answers
52
views
Numerically solved PDE of Ornstein–Uhlenbeck process on 2-Simplex violates conservation of probability [closed]
Thanks for your consideration.
I'm working to create a solution of an Ornstein-Uhlenbeck process with a force that takes mass towards the centre of a Simplex. I'm assuming absorbing boundaries.
The ...
- 15
0
votes
0
answers
26
views
Uniform initial conditions make Fokker-Planck/Kolmogorov Equation boundary conditions inconsistent
When considering the time evolution of a distribution over a state variable $x$, one of the cases that seems fundamental is when knowledge about $x$ begins uniform. However, modelling the process as ...
- 15
0
votes
0
answers
49
views
Mathematica PDE solving
I'm new to Mathematica and have never solved a PDE before. I tried to follow a textbook to get equation 4, but got something different with Mathematica (I got $(4\pi Dt)^{1/2}$ instead of $(4\pi Dt)^{...
- 169
-4
votes
1
answer
68
views
Can you help me to solve this PDE? [closed]
Could you please help me to solve the following equation?
\begin{equation}
u_{yyyy}+u_{xy}-a\,\left(u\,u_y\right)_y\,=\,0
\end{equation}
Where
\begin{equation}
u\,=\phi^{\alpha} \sum_{k\,=\,0}^{\...
- 1
0
votes
1
answer
138
views
Partial Differential Equation on a Riemannian Manifold: How to solve complex second order ODE by hand.
I'm working on a project where I discuss using the metric tensor to compute the Laplacian on various Riemannian Manifolds, and how that can aid in solving certain Partial Differential Equations. In ...
2
votes
1
answer
241
views
How to solve this biharmonic equation? (Viscous fluid flow)
I am investigating lid-driven cavity flow, demonstrated in the below diagram:
We have a square (two dimensional) domain, with fully Dirichlet conditions for the velocity and fully Neumann conditions ...
- 12.5k
3
votes
0
answers
89
views
How to find eigenvalues of a linear operator consists of laplacian?
I have the following matrix of linear operator consists of Laplacian \begin{bmatrix}0&1&0\\\Delta&\Delta& 0\\0&0&\Delta\end{bmatrix}
acting on \begin{bmatrix}w\\w_t\\u\end{...
- 31
1
vote
0
answers
72
views
How to solve simple 2D space-time PDE numerically
I have a 2D space-time PDE and I want to solve it numerically over the time axis. The time initial field is already known with respect to space, i.e., the spatial distribution is already known at time ...
- 109
4
votes
0
answers
184
views
How Can I Visualize a PDE Boundary Condition?
In this question, the comment suggests that the integration bounds in the Fourier Series should be chosen to avoid discontinuities in the boundary conditions. I am trying to produce a nice visual to ...
- 1,922
1
vote
1
answer
129
views
Analytical solution for a difficult nonlinear PDE
Is it possible to compute the analytical solution for this nonlinear pde? It doesn't seems to work with Sympy but it doesn't i can do it with it. The point is to prove that the convergeance order of ...
- 71
0
votes
1
answer
107
views
Numerically Solve PDE
I am looking for some help finding a numerical solution to a pde of the form:
$$C_t=f(x)C_x+\alpha C_{xx}$$
with initial condition for $C(x,t)$:
$$C(x,0)=\delta(x)$$
and boundary condition
$$C(\pm\...
- 119
3
votes
1
answer
156
views
How to find solve for second order pde with initial conditions using Wolfram Mathematica?
I have next task:
$$
\frac{\partial^2 u}{\partial x \partial y} = 0,~ u(x,x^2) = 0,~ \frac{\partial u}{\partial x}(x, x^2) = \sqrt{|x|},~|x| < 1
$$
I write this, but it don't work:
...
- 43
0
votes
1
answer
93
views
How to use the Wolfram Language or another tool to find a second order pde solution with initial conditions?
I want to find a solution the Cauchy problem using the Wolfram Language or some other tool.
I have next task:
$$
3\frac{\partial^2 u}{\partial x^2} + 8\frac{\partial^2 u}{\partial x \partial y} - 3\...
- 43
1
vote
1
answer
3k
views
Analytical solution for convection diffusion equation
Convection-diffusion equation is:
$\frac{\partial u}{\partial t} + \frac{\partial u}{\partial x} = 0.01\frac{\partial^2 u}{\partial x^2}$
Inital conditon is:
$u(x,0) = sin(x)$ over the domain 0 to $...
- 215
2
votes
2
answers
953
views
Solve parametric differential equation using Mathematica
Using the method of characteristics on a PDE system, I have gotten a parametric differential equation
$$
\frac{dy}{dx} = \frac{y - xy}{1 + xy - x}.
$$
where $x$ and $y$ are both functions of a third ...
- 259