The Solution of Linear Constant-Coefficient Evolution PDEs With Periodic Boundary Conditions

We implement the new transform method for solving boundary value problems developed by Fokas for periodic boundary conditions. The approach presented here is not a replacement for classical methods nor is it necessarily an improvement. However, in addition to establishing that periodic problems can indeed be solve by the new transform method (which enhances further its scope and applicability), our implementation also has the advantage that it yields a new simpler approach to computing the limit from the periodic Cauchy problem to the Cauchy problem on the line.