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We present the numerical solution of two-point boundary value problems for athird order linear PDE, representing a linear evolution in one space dimension.The difficulty of this problem is in the numerical imposition of the boundaryconditions, and to our knowledge, no such computations exist. Instead ofcomputing the evolution numerically, we evaluate the solution representationformula obtained by the unified transform of Fokas. This representationinvolves complex line integrals, but in order to evaluate these integralsnumerically, it is necessary to deform the integration contours usingappropriate deformation mappings. We formulate a strategy to implementeffectively this deformation, which allows us to obtain accurate numericalresults.

A numerical implementation of the unified Fokas transform for evolution problems on a finite interval