On the solution of forward and inverse problems of voltammetry Nikolay Koshev ∗ Abstract Inverse problem of voltammetry of simple electrolytes (aqueous solutions of electro-active com- ponents) is the coefficient inverse problem for the partial differential equation (PDE) of parabolic type. Since most algorithms for solution of such problems are based on the discrepancy minimization, their efficiency strongly depends on the way of calculation of the forward problem. In this paper we formulate forward and inverse problems of voltammetry, then consider three different algorithms of solution of the voltammetry equation, including developed by author semi-analytical method. 1 Introduction Voltammetry is an important method of electrochemical analysis which is based on measuring of the de- pendence of current on the potential. Voltammetry is used to study physico-chemical processes occurring in systems, which contain electrolytes or other electro-active components. Detailed physical and chemical description of the process of voltammetry is presented in [1]. In this paper we consider forward (direct) and inverse problems of voltammetry. The forward problem consists in modelling of products of the process with known parameters such as initial and boundary condi- tions, concentration of components, speed of sweeping of the potential etc. Under the products of the process we suppose, for example, mass transfer or direct current. The forward problem is very well known and is considered in many works (see, for example, [2]). The goal in the solution of inverse problem (IP) is calculating of the described parameters and values on the base of voltammetry curve, obtained experimentally within the process of voltammetry. In this paper we consider important IP for calculating of concentrations of metal ions in the process of the electrolysis. This IP was not studied widely, but some attempts to formulate and solve this problem are presented, for example, in [3]. Since most algorithms for solution of such problems are based on the discrepancy minimization, their efficiency strongly depends on the numerical technique for the solution of forward problem. In this paper we consider and compare different approaches for modelling of the voltammetry process and propose the method based on using source or Green functions, which is convenient for the numerical solution of IP. Nikolay Koshev * Department of Physics, Penza State University of Architecture and Building, Russian Federation, e-mail: niko- lay.koshev@gmail.com 1