This book deals in a simple manner with the numerical solution of parabolic partial differential (diffusion) equations as they appear in electroanalytical chemistry, but extends also to the more sophisticated and efficient techniques. Only a basic familiarity with mathematics is assumed. It is intended both as an elementary text for the beginner as well as a reference for the more experienced. It incorporates the newer methods such as orthogonal collocation, unequal intervals, hopscotch, Runge-Kutta integration of semidiscretised systems of equations, and implicit boundary value calculation, which is required for the Crank-Nicolson technique to be effective in this field, where derivative boundary conditions are the rule. This second edition has been updated extensively to take into account recent developments in the area. It also deals squarely with the problems resulting from homogenous chemical reactions. With the help of this book and its many programming examples, any electrochemist should be able to learn to use the technique quickly in its simpler forms and will hopefully be stimulated to learn about the more difficult methods later.