(untitled) (Journal of Computational Mathematics, 2018)
This paper deals with an inverse problem of a system of ordinary differential equations whose coefficient matrix is the so-called compartmental matrix.This problem arises in a variety of areas such as pharmacokinetics, biology, economics, and so on. A numerical method applicable to the cases of non-unique solutions is developed, by which the projection of the starting value of iteration onto the manifold of solution can be obtained. The convergence of the method is proved. A few examples are examined, which shows the effectiveness of the given method.