The diffusion problem

Abstract

The study of diffusion processes is relevant in various fields: chemistry, physics, metallurgy, medicine, and others. The paper considers and solves the problem of diffusion of charged particles under the action of an electromagnetic field in a semi-infinite thin tube. The mathematical formulation is a boundary value problem for an inhomogeneous partial differential equation of the parabolic type. To obtain an accurate analytical solution, the operator method is used. The solution is initially obtained in the form of an image, and then the solution of the original problem is obtained using the inverse Laplace transform. The solution of the test example is obtained, a graphical image of the desired function is constructed in the MatLab software package.