Hermitian Characteristic Scheme for a Linear Inhomogeneous Transfer Equation

Abstract

In this paper, we design an interpolation-characteristic scheme for the numerical solution of the inhomogeneous transfer equation. The scheme is based on the Hermitian interpolation to reconstruct the value of an unknown function at the point of intersection of the backward characteristic with the cell faces. The Hermitian interpolation to reconstruct the function values ​​uses both the nodal values ​​of the desired function and its derivative. Unlike previous studies also based on the Hermitian interpolation, not only the differential continuation of the transfer equation but also the relationship between the integral averaged values, nodal values, ​​and derivatives according to the Euler-Maclaurin formula is used to transfer information about the derivatives to the next layer. The third-order difference scheme is shown to converge for smooth solutions. The dissipative and dispersive properties of the scheme are considered using numerical examples of solutions with decreasing smoothness.