Intelligent instrumentation and numerical methods

In this paper we discuss the choice of numerical methods that yield the least numerical error for a given number of discretized spatial nodes, and a proper eigenvalue procedure that avoids numerical integration in time with the corresponding saving in computer requirements. These procedures are suited for small computing systems to be used in field instrumentation. We check the effectiveness of these methods with the solution of a diffusion equation with recombination, time dependent and in one dimension in space. We compare the results obtained with a second order finite difference scheme with those obtained with a spectral method solution, showing the superiority of the last approach.