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.