Numerical Methods for Solving Boundary Value Problems for the Generalized Integro-differential Modified Moisture Transfer Equation with the Bessel Operator

Abstract

Initial-boundary value problems for the generalized integro-differential modified moisture transfer equation with the Bessel operator are investigated. Difference schemes are constructed that approximate these problems on uniform grids. The case of an equation is considered in which the coefficients of the highest derivatives are separated from zero by a positive constant. For the solution of the problems under consideration, a priori estimates are obtained in differential and difference interpretations. The obtained estimates imply the uniqueness and stability of the solution with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem. An algorithm for finding approximate solutions of the problems under consideration is constructed and numerical calculations of test examples are carried out, illustrating the theoretical calculations obtained in the work.KeywordsBoundary value problemsA priori estimateMoisture transfer equationIntegro-differential equationFractional-order differential equationFractional Caputo derivative