# Tag Info

Accepted

### How do I simulate an open end?

The problem you describe, how to prescribe non-reflecting or absorbing boundary conditions when solving partial differential equations (PDE) has been extensively studied. For complex (e.g. nonlinear) ...
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### How to solve a second order differential equation (diffusion) with boundary conditions using Python

I have found that I must keep the value of dt near dx or the results become unstable This behavior you have noticed is known as the Courant–Friedrichs–Lewy (CFL) condition. Indeed, there are ...
• 1,124
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### Symmetric boundary condition

For the sake of simplicity let me slightly change your notation. Let $u, v, w$ be the components in the $x, y, z$ directions of a true (polar) vector, and $y=0$ the symmetry plane. For a true vector, ...
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• 901
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### How to apply non zero Dirichlet boundary condition in finite elements?

Consider the fact that your linear system can be broken up into two parts: the equations that correspond to the known Dirichlet dofs, and the equations that correspond to the unknown dofs. For the ...
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• 380
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### Structural mechanics - traction free = Zero displacement gradient?

The traction is defined as $$\mathbf{t} = \mathbf{n} \cdot \boldsymbol{\sigma}$$ In terms of components, the zero-traction condition is $$t_j = \sum_i n_i \sigma_{ij} = 0$$ From the above ...
Accepted

### Radiation boundary condition (heat transfer)

This is not particularly difficult once you realize that the nonlinear boundary condition simply yields a nonlinear term in the weak formulation. Let's assume that you want to solve the steady state ...
• 56.2k
If you convert the first line of your matrix operator back into a difference equation you get $$2y(x)-y(x+h)=h^2b,$$ where $b$ is whatever is on the right hand side. This is consistent with a non-...