AN EFFICIENT NUMERICAL-METHOD OF SOLVING INTEGRAL-EQUATIONS FOR CYCLIC VOLTAMMETRY

The previously proposed numerical algorithm for solving the Abel integral equations for cyclic voltammetry has been generalized to allow solutions of more complicated cyclic voltammetric integral equations. The algorithm is based on a semi-integration procedure, resulting from the accepted approximation for the factor (zeta - z)-1/2 in the kernel functions W(zeta, z)(zeta - z)-1/2 Which is valid for zeta - z is-an-element-of [0.00155, 30]. The Newton iterative method is additionally used to handle non-linear integral equations. The algorithm can be applied to kinetic problems which relate to one- or two-electrode reactions and one-dimensional diffusion and adsorption. Moderately rapid homogeneous reactions are also acceptable, provided that the non-dimensional time variables zeta and z are separated in the functions W(zeta, z). Several example integral equations have been solved, showing that the algorithm is faster by one to three orders of magnitude than traditional product-integration methods at much lower memory requirements and with satisfactory accuracy.