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Abstract
The method of separation of variables is a powerful tool for solving equations of mathematical physics but it can seldom be used in practical situations. In this paper we present the amplitude-shape method which can be viewed as an incomplete separation of variables so that the solution to a given equation is written as a product of a fast-changing amplitude and a slow-changing shape to overcome the difficulties associated with stiffness caused by singular perturbations. The method is closely related to the quasistatic approach developed and successfully used in nuclear reactor kinetics. We show the implementation of the method for partial differential equations of the chemical kinetics.