I would like to numerically simulate a wave (let's say in a string) with different boundary conditions:
- Fixed endpoints
$\varphi(x, t)$ is the value of the wave (vertical position of the string) at pixel $x$ captured by a 1-D array
phi. For fixed endpoints, I simply pad my array with a zero on the left and one on the right (for numerical differentiation purposes). For the periodic boundary, I pad the left side with the last element (
phi[-1] in Python syntax) and I pad the right side with the first element (
How do I handle the boundless case so a pulse would just travel without reflection similar to the figure below? What is the common term for this type of boundary? (I do not want to sufficiently increase the number of pixels to solve this problem).