Amplitude-shape method: The quasistatic method revisited

Abstract

The numerical solution of large stiff systems of ordinary differential equations is very expensive and requires large and fast computers. This is painfully clear to all who attempt to solve numerically nuclear reactor kinetics equations. The discrete form may involve as much as 100 000 ordinary differential equations and the stiffness is supplied by prompt neutrons. No wonder that reactor physicists were for years looking for some sort of simplification and this came about in the middle of the 60' as the widely used quasistatic method. Unfortunately, it had been based upon purely heuristic grounds and never left the realm of the reactor physics remaining completely unknown for the specialists in numerical solution of ordinary differential equations. In this article we show that the amplitude-shape method (ASM) which takes from the quasistatic method the representation of the solution as the product of the fast chaiiging amplitude and slow varying shape function, can be used in tlie reactor kinetics. The ASM whose full exposition is given in [5], has been developed to be applicable for numerical solution of a large class of systems of ordinary differential equations and is particularly useful in case of partial differential equations describing thc evolution of physical systems. In this paper we present the application of the ASM to the reactor kinetics equations. We present the numerical results for model equations and show that the ASM works equally well for subcritical or for supercritical systems. From [5] it follows the ASM can be also used for nonlinear problems of nuclear reactor dynamics. Practical implementation of the ASM in reactor codes is being currently investigated.