A simple, fast numerical method for the solution of a wide variety of electrochemical diffusion problems

A numerical analysis technique known as orthogonal collocation, which has found considerable use in solving linear and non-linear partial differential equations in chemical engineering, is applied to a variety of boundary value problems found in chronoamperometry. Due to the properties of the collocation functions, the technique requires very little implicit mathematics and results in a large savings in computer time over the common digital simulation technique or the Crank-Nicholson finite difference scheme. Simulation of a new boundary value problem requires only a few operations of calculus and matrix algebra and alteration of very few program statements. The computer program employed is quite simple and is composed almost entirely of highly efficient library subroutines. Due to the nature of the orthogonal polynomials used to represent the spatial dependence of concentration, the trial function exactly fits the partial differential equation at the collocation points and transforms it into a set of simultaneous first order ordinary differential equations. These equations are solved numerically in about 5 s on a CDC 6600 to give accurate working curves (≈0.1% error or less) for the e.c.e. and for first and second order disproportionation mechanisms at a planar electrode.