  We implement the Unified Transform Method of Fokas as a numerical method to
solve linear partial differential equations on the half-line. The method
computes the solution at any x and t without spatial discretization or time
stepping. With the help of contour deformations and oscillatory integration
techniques, the method's complexity does not increase for large x,t and the
method is more accurate as x,t increase. Our goal is to make no assumptions on
the functional form of the initial or boundary functions while maintaining high
accuracy in a large region of the (x,t) plane.
