Numerical Solution of the Inverse Nonequilibrium Sorption Problem with a Time-Dependent Boundary Condition

We consider the quasi-linear problem of nonequilibrium sorption dynamics with external-diffusion kinetics and a boundary condition that contains the time derivative of a solution component. A numerical method is proposed for describing the inverse problem to recover the nonlinear parameter of the system of differential equations—the inverse of the sorption isotherm. Convergence of the difference scheme for the direct problem is proved. Numerical solutions of both the direct and the inverse problem are obtained for various parameter values.