Reducing computational time via order reduction of a class of reaction-diffusion systems

In this paper, we consider a class of reaction-diffusion PDEs. For this class, a suitable state transformation allows conversion to a heat equation together with a lower order PDE set. By giving an explicit solution to the heat equation we are able to obtain a complete solution to the original PDE. By focusing on the computational load, we give a comparison of the pure numerical, analytical/numerical, analytical/approximated, and approximated methods of solving the PDE. In some examples, we note an almost order of magnitude improvement in computational load.