Analytic-numerical solutions of mixed problems for coupled systems of generalized diffusion equations with delay

REFERENCES [1] Wu, J. Theory and Application of Partial Functional Differential Equations. Springer Verlag, New York, 1996. [2] Martín, J.A., Rodríguez, F., Company, R. Analytical solution of mixed problems for the generalized diffusion equation with delay. Mathematical and Computer Modelling, 40 (2004), 361--369. [3] Reyes, E., Rodríguez, F., Martín, J.A. Cálculo eficiente de soluciones numéricas continuas de problemas mixtos para la ecuación generalizada de difusión con retardo. XIX CEDYA/IX CMA, Madrid, 2005. ACKNOWLEDGEMENTS This work has been partially funded by Valencia Regional Government (Generalitat Valenciana), trough projects GV04B/454 (Conselleria de Cultura, Educación y Deporte) and GV06/207 (Conselleria de Empresa, Universidad y Ciencia). We thank the University of Alicante for financial support to the Delay Differential Equations research group. ABSTRACT This work deal with the construction of analytic-numerical solutions of mixed problems for systems of generalized diffusion equations with delay of the type ( , ) ( , ) ( , ), , 0 , t xx xx u t x Au t x Bu t x t x l τ τ = + − > ≤ ≤ where A and B are constant matrices, in general not simultaneously diagonalizable. A separation of variables method is used to develop an exact theoretical series solution, which can be truncated to obtain a continuous numerical solution with prescribed accuracy in bounded domains.