Application of the projection-grid method for solving nonstationary problems

The work is devoted to constructing approximate solutions of a parabolic differential equation with the Bessel operator. Solutions are sought in the form of a linear combination of piecewise continuous, compactly supported basis functions. The construction of the solution is performed in two stages. Initially, the approximation in a spatial variable is performed by using the Bubnov–Galerkin projection-grid method. Then the approximation in $t$ is carried out by using the finite-difference method. The resulting system of equations is solved by the tridiagonal matrix algorithm.