Features of the implementation of a modified scheme with Hermitian interpolation for the numerical solving of the transport equation with a variable absorption coefficient

The grid-characteristic scheme based on Hermitian interpolation is used for solving the transport equation with a varying absorption coefficient. Hermitian interpolation is built on the previous time layer using the nodal values of the function itself and its spatial derivatives. To calculate the nodal values of the space derivative on the new time layer the integral averages and the Euler–Maclaurin formula relating nodal values, integral average and derivative values at nodes are used. Convergence tests for various smoothness functions were carried out. It is shown that at the points of the absorption coefficient discontinuity it is most accurate to use the absorption coefficient in the cell where backward characteristic lies.