Numerical-analytical method for solving boundary value problem for the generalized moisture transport equation

Abstract

The paper studies qualitatively new equations of moisture transfer, which generalize the Aller and Aller-Lykov equations. The generalization contributes to revealing in the original equations the specific features of the studied massifs, their structure, physical properties, processes occurring in them through the introduction of the notion of the rates of change of the fractal dimension. We have obtained solutions to the constant coefficient difference equations as a system arising when using the method of lines for the equations with a Riemann-Liouville time fractional derivative with boundary conditions of the first kind. A priori estimates are obtained that imply convergence of the obtained solutions to systems of ordinary differential equations with variable fractional coefficients. Numerical tests have been carried out to confirm theoretical results of the study.

Local and nonlocal boundary value problems for generalized Aller - Lykov equation

“…In [10] for generalized Aller and Aller-Lykov equations with Dirichlet boundary conditions there were obtained solutions for a system of difference equation with constant coefficients arising while using the methods of straight lines. There were obtained apriori estimates, which implied the convergence of solutions to a system of ordinary fractional differential equations with varying coefficients.…”