Approximate solution of the first boundary value problem for the loaded heat conduction equation

The first boundary value problem for the loaded heat equation with variable coefficients is studied. For the numerical solution of the problem posed, a difference scheme of a high order of accuracy is constructed. An a priori estimate in difference form is obtained by the method of energy inequalities. This estimate implies 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 original differential problem at arate of 𝑂(ℎ4 +τ2). An algorithm for the approximate solution is constructed, and numerical calculations of test examples are carried out, illustrating the theoreticalresults obtained in the work.