# Questions tagged [boundary-conditions]

For questions regarding the choice and/or appropriateness of conditions necessary to model a particular phenomenon with a partial differential equations.

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### Multigrid stops converging when more grid levels are used

I'm having a problem with multigrid code I wrote. If I solve Laplace's equation in 2D and use more than 5 grid levels, the V-cycles stop converging after a few cycles (see below, convergence factor > ...
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### Determine numerical infinity for Schrodinger equation $−\psi''(x) + x^ 2 \psi(x) = E\psi(x)$

Consider the following Schrodinger equation for the harmonic oscillator with real $x$: $$−ψ''(x) + x^ 2 ψ(x) = Eψ(x).$$ I solve the last equation using shooting method and implicit Runge-Kutta ...
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### Apply second order finite difference discretization for mixed boundary condition

I want to solve the problem below \begin{aligned} \eta u-\Delta u &=f, &\text{in \Omega}\\ \end{aligned} where \$\Omega=(0,1)\times (...
I am solving the 1D advection problem given by: $$\frac{\partial u}{\partial t}=-c\frac{\partial u}{\partial x}$$ where c is the wave speed, and u is the unknown field variable, and x and t are time ...