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### NDSolve boundary condition relating derivatives in different variables [duplicate]

I am trying to solve a wave equation (2nd order PDE) in z and t with absorbing boundary conditions, i.e. a boundary condition that relates the partial z and t derivatives. For this particular example,...
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### Specify direction of propagation in the 1-d wave equation in NSolve and NDSolve [duplicate]

I am solving the 1-d wave equation with the following initial conditions: ...
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### Boundary Condition for Schrödinger Equation in Infinite Range

I am trying to simulate the movement of a coherent state in a quantum harmonic oscilator, but for some reason the answer diverges and there is a warning about not enought boundary conditions. Also, ...
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### Numerical solutions of active 1D wave equations

I would like to solve the following PDE with finite difference method. The PDE is from the following paper, (https://arxiv.org/pdf/1911.11823.pdf). I would like to implement the algorithm for the left ...
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### Workarounds for a possible bug in the linearity of FourierTransform

This is somewhat similar to this question, except the problem I am encountering is to do with Fourier transforms of scalar multiples of functions and their derivatives. I wish to input ...
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### What boundary is added when boundary condition is not sufficient?

When insufficient boundary conditions are given to NDSolve for solving PDE, usually the warning NDSolve::bcart pops up: ...
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### 1D-waveequation with absorbing boundary condition: FEM solution?

I try to simulate the special absorbing(?) boundary condition Derivative[1, 0][y][1, t] + Derivative[0, 1 ][y][1, t] == 0 which only allows energy flow in ...
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### Forcing at least $n$ spatial steps in solving a 1D spatio-temporal PDE problem with NDSolve

I want to solve the telegraph equation with a spatial discretization forced at 200 points. I tried: ...
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### Half-absorbing boundary conditions

I'm trying to solve the spherically symmetric wave equation $$0 = (\partial_t^2 - \partial_r^2 + 1)\phi(t,r)\,,$$ where $\phi(t,0) = 0$. Without doing anything fancy, we can solve this equation "...
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In general, when solving a 2nd order PDE (such as the wave equation below) for $$u(x,t), \quad x \in(-\infty,\infty), \: t\in (0,\infty)$$ it should be sufficient to provide initial conditions $u(x,0)$...