A new method for the solution of initial-boundary value problems forevolution PDEs recently introduced by Fokas is generalised to multidimensions.Also the relation of this method with the method of images and with theclassical integral transforms is discussed. The new method is easy toimplement, yet it is applicable to problems for which the classical approachesapparently fail. As illustrative examples, initial-boundary value problems forthe diffusion-convection equation in one and higher dimensions, as well as forthe linearised Korteweg-de Vries equation with the space variables on thehalf-line are solved. The suitability of the new method for the analysis of thethe long-time asymptotics is ellucidated.
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