Abstract
An adaptive collocation method is introduced for simulating the short time diffusion–convection-reaction problem. The method is based on dividing the solution domain into active and inactive zones in such a way that the collocation points remain concentrated in regions of solution variation. The numerical results show that the proposed method is efficient in simulating the sharp profile at short time for the convective-dominant case. The adaptive scheme performance is found compatible with the high-order finite difference method, the QUICK method in terms of the CPU time and average numerical errors.