# Questions tagged [parabolic-pde]

A partial differential equation that describes diffusion phenomena.

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### "Optimal" domain partitioning in domain decomposition algorithms

When solving a PDE numerically by domain decomposition methods, what is the "optimal way" to split the domain? Are there any results stating that a particular partition of the domain yields &...
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### Derivation of a parabolic PDE using Alternating Direction Implicit method

I have a very simple question concerning Alternating Direction Implicit (ADI) Scheme. If I have an equation of the form: \begin{equation*} \frac{df(x,y,t)}{dt} = \nabla^2 f(x,y,t) + f(x,y,t) \end{...
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### 3d schrodinger equation weak form

SCHRODINGER’S EQUATION $$-ih u_{t}(x,y,z,t) = \frac{h^2}{2m} u_{xx}(x,y,z,t)+ \frac{e^2}{r}u(x,y,z,t)$$ The potential $\frac{e^2}{r}$ is a variable coefficient. So, let’s take the free Schrodinger ...
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### 1D FEM for nonlinear diffusion coefficient

I want to solve with linear finite elements the equation $$\partial_t u = \partial_{x}(a(u)\partial_xu)$$ in the domain $t \in [0,1]$ and $x \in [-L,L]$. Here $a(u)$ is just a function of $u$. ...
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### Type of Rosenbrock method by its coefficients

A Fortran code that solves stiff PDE systems contains the following arrays of Rosenbrock-Wanner method coefficients: ...
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### How suitable is multigrid method for time-dependent PDEs?

For elliptic PDEs (Poisson-type), the multigrid method is very sufficient, but how about time-dependent problems (i.e parabolic or hyperbolic PDEs)? Is it efficient to solve such problems using a ...
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### Solving Parabolic PDE using Matlab

I have the following pde (Burger's equation) for $\epsilon>0: u_t+u.u_x=\epsilon.u_{xx}$ and $x\in \mathbb{R},t>0$ and the initial condition: $u(x,0)=\phi(x)=1_{(-\infty,0)}(x)$. I want ...
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