On numerical solution of spatially extended dynamical systems with time-delay

A novel algorithm for optimizing storage of intermediate space fields in the numerical simulation of evolution of spatially extended time-delayed systems by finite difference method is proposed. The algorithm involves storing in the memory not all, but only some selected time layers, and the subsequent interpolation of the data in the construction of intermediate layers. This approach allows the numerical calculations to be implemented on computer systems without large memory. The effectiveness of the developed algorithm is demonstrated by the example of numerical simulation of the transcription of proteins that determine circadian rhythms in cells.