Mathematical Model of a pH-gradient Creation at Isoelectrofocusing. Part II. Numerical Solution of the Stationary Problem

TL;DR

This paper develops a numerical method to solve the stationary pH-gradient creation problem in isoelectrofocusing, addressing the challenges of stiffness and validating solutions at high voltages or current densities.

Contribution

It introduces a shooting method for numerically solving the stiff boundary value problem in pH-gradient modeling, extending previous theoretical work.

Findings

Numerical solutions match weak solutions at high voltages.

The method effectively handles stiffness due to small parameters.

Validation against theoretical solutions confirms accuracy.

Abstract

The mathematical model describing the natural textrm{pH}-gradient arising under the action of an electric field in an aqueous solution of ampholytes (amino acids) is constructed and investigated. This paper is the second part of the series papers \cite{Part1,Part3,Part4} that are devoted to pH-gradient creation problem. We present the numerical solution of the stationary problem. The equations system has a small parameter at higher derivatives and the turning points, so called stiff problem. To solve this problem numerically we use the shooting method: transformation of the boundary value problem to the Cauchy problem. At large voltage or electric current density we compare the numerical solution with weak solution presented in Part 1.