Hello I am interested in smoothing out the sharp edges of a single rectangular wave centered at the origin.

I am looking for a smooth function that looks almost exactly the same as the square wave except it is differentiable everywhere.

I looked at Fourier Series but this creates a periodic function which I do not want. I want to create a rectangular wave of finite height and zero everywhere else.

Ultimately, I want to plug this approximating function into NDSolve in attempt to get rid of "spiky" effects present in the solution of the wave equation.

Thank You!

Hello I am interested in smoothing out the sharp edges of a single rectangular wave centered at the origin.

I am looking for a smooth function that looks almost exactly the same as the square wave except it is differentiable everywhere.

I looked at Fourier Series but this creates a periodic function which I do not want. I want to create a rectangular wave of finite height and zero everywhere else.

Ultimately, I want to plug this approximating function into NDSolve in attempt to get rid of "spiky" effects present in the solution of the wave equation.

Thank You!

Edit::

This is the square pulse in question: