Abstract: The time integration method with four-order accuracy, self-starting and implicit for the diffuse chemical reaction kinetics equation or the transient instantaneous temperature filed equation was presented. The examples show that both accuracy and stability are better than Runge-Kutta method with four-order. The coefficients of the equation are stored with sparse
matrix pattern, so an algorithm is presented which combines a compact storage scheme with reduced computation cost. The computation of the competitive and consecutive reaction in the rotating packed bed, taken as examples, shows that the method is effective.

Key words: step-by-step integration, diffuse, chemical reaction kinetics, rotating packed bed, micro-mixing