It was confirmed that the results given by the integral factor method showed the delaying of response in the numerical experiments using the advection-diffusion equation. However, the exponential solutions given by the integral factor method were not very smooth compared to the analytically correct solution. On the other hand, a delay in the exponential solution was clearly found for an increasing time increment. Therefore it is important to make the time increment shorter step by step, to check the delaying when applying this integral factor method. It would be expected that the exponential solution given by the integral factor analysis method shown here would have the same expression. That would mean that this method had great potential and could be widely used.

integral factor method, exponential Taylor method, advection–diffusion equation