Numerical Study of Higher Order Perturbation Theory

The higher order perturbation theory is studied numerically. The one-dimensional diffusion equation is solved by the conventional (1st order) and the higher order (2nd and 3rd order) perturbation methods. The results are compared with those exactly calculated, and the accuracy, the effect of the higher order terms and limit of the perturbation method are examined. When the perturbation in the reactor is non-uniform, the higher order perturbation method is found to be effective. When the perturbation is uniform, however, the higher order terms are of relatively small importance.