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The simultaneous set of partial differential equations – two mass transport equations and the Poisson equation – have been solved using finite-elements.
In this paper the two-point boundary value problem is transformed into general first-order ordinary differential equation system through introduction of conditions of an integral character to supplement the simultaneous set of first-order equations.
The aim of the work is to stress the impact of the use of rigorous numerical methods, today possible for the high performances reached by the computers, in the solution of a simultaneous set of many differential equations that are necessary to describe completely the mentioned system.
The fundamental difference between the new method and other methods based on a first-order approach is the introduction of conditions of an integral character to supplement the simultaneous set of first-order equations, which are hence never regarded as an initial value problem.
This will be referred to as a 'simultaneous set' , and each system of the simultaneous set will be called a 'member system' (=m-system).
The second system, called sphere of action, consists of a simultaneous set with three m-systems.
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