Fokas method for a multi-domain linear reaction-diffusion equation with discontinuous diffusivityFokas method for a multi-domain linear reaction-diffusion equation with discontinuous diffusivity Πλήρης Δημοσίευση σε Συνέδριο Conference Full Paper 2015-10-162013enMotivated by proliferation-diffusion mathematical models for studying highly diffusive brain tumors, that also take into account the heterogeneity of the brain tissue, in the present work we consider a multi-domain linear reaction-diffusion equation with a discontinuous diffusion coefficient. For the solution of the problem at hand we implement Fokas transform method by directly following, and extending in this way, our recent work for a white-gray- white matter brain model pertaining to high grade gliomas. Fokas’s novel approach for the solution of linear PDE problems, yields novel integral representations of the solution in the complex plane that, for appropriately chosen integration contours, decay exponentially fast and converge uniformly at the boundaries. Combining these method-inherent advantages with simple numerical quadrature rules, we produce an efficient method, with fast decaying error properties, for the solution of the discontinuous reaction-diffusion problem.http://creativecommons.org/licenses/by/4.0/ Proceedings of IC- MSQUARE Conference on Mathematical Modeling in Physical Science M. Asvestas Sifalakis Anastasios Σηφαλακης Αναστασιος Papadopoulou Eleni Παπαδοπουλου Ελενη Saridakis Ioannis Σαριδακης Ιωαννης IOP Publishing Greek mathematics mathematics greek greek mathematics