On the numerical analysis of analytical nodal methods

This article presents the basic numerical analysis of the analytical nodal methods, which were originally developed in the late 1970s in relation with static and dynamic nuclear reactor calculations but are actually applicable to the numerical solution of partial differential equations (PDEs) in general, over fairly regular domains. The basic idea consists in “transverse integrating” the original PDE over all the variables minus one, leading to sets of 1D equations which are then solved in an “analytical” way, using fundamentals as well as particular solutions of the corresponding 1D operators. After examining the existing analytical methods in a critical way, we propose a more satisfactory extended analytical formalism. Superconvergence results finally lead us to useful conclusions with respect to the choice of a particular scheme.