Abstract
We present the numerical solution of twopoint boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary conditions, and to our knowledge, no such computations exist. Instead of computing the evolution numerically, we evaluate the solution representation formula obtained by the unified transform, also known as Fokas transform. This representation involves complex line integrals, but in order to evaluate these integrals numerically, it is necessary to deform the integration contours using appropriate deformation mappings. We formulate a strategy to implement effectively this deformation, which allows us to obtain accurate numerical results.
Original language  English 

Pages (fromto)  543567 
Number of pages  25 
Journal  European Journal of Applied Mathematics 
Volume  29 
Issue number  3 
Early online date  23 Nov 2017 
DOIs  
Publication status  Published  Jun 2018 
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Beatrice Pelloni
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)