A hybrid solution method for an inverse problem for the general transport equation

Abstract

In this work, we deal with an inverse source problem for a general transport equation. First, we discuss the solvability of the problem. Next, in order to solve the problem, we propose a new hybrid numerical algorithm which is based on the finite difference method, Newton-Cotes formula, Lagrange polynomial approximation and composite trapezoidal rule. The proposed method is tested on several examples and the results show that the relative errors in the computation are sufficiently small and the algorithm is robust to data noises.