I am building an PDE solver and would like some PDEs to test it on. However to test it works I want to compare it to exact solutions but I'm not having much luck finding these online. I currently have
- diffusion equation with time-varying boundaries
- wave equation with constant boundaries
however I would like to also test
- diffusion equation with no-flux boundaries
- advection-diffusion equation with mixed boundaries
- advection-diffusion equation with constant boundaries
- kvd equation with any boundaries
- benjamin-bona-manhony equation with any boundaries
however I am having trouble finding suitable initial conditions and an exact solutions to these. Any suggestions of initial conditions/boundary conditions/exact solutions would be very much appreciated. If you have any exciting equations you like I would also love to hear!