Numerical Analysis of Python Optical Simulation how to solve Wave equation and draw Wave packet variation Diagram

This article introduces the relevant knowledge of "Python optical simulation numerical analysis how to solve wave equation and draw wave packet change diagram". In the operation process of actual cases, many people will encounter such difficulties. Next, let Xiaobian lead you to learn how to deal with these situations! I hope you can read carefully and learn something!

numerical solution of wave equation

Wave equation is one of the three physical equations, namely string vibration equation, which is characterized by second order partial derivatives in time and space. The free-space solution is known as trigonometric function, and can also be written in natural imaginary exponential form.

Generally speaking, since there is an accurate analytical solution, there is no need to do imprecise numerical simulation, but there are two advantages of numerical simulation, one is to avoid infinitesimal, so that more intuitive in thinking; the other is quite enlightening, for some analytical solutions also have a certain ability to deal with.

For this, we first consider the one-dimensional wave equation

import numpy as npimport matplotlib.pyplot as pltdef set_y0(x,k,L): y = np.zeros_like(x) y[x