Analytic solution of the 1d Wave Equation

Computing the exact solution for a Gaussian profile governed by 1-d wave equation with free flow BCs or with perfectly reflecting BCs.

I constructed this solution to verify the accuracy and stabitlity of some FD-compact schemes.

This solution, was obtained throught greens function approach using the method of images. (These details are not given here. I only write/compute the final expression from the analysis).

I believe, it will be very usefull for those looking to verify the accurary of numerical boundary conditions of linearized froms of Euler and/or Navier-Stokes equations.

Happy coding! : )