Solution of Homogeneous Systems of Linear Equations Arising from Compartmental Models

Abstract

Systems of linear differential equations with constant coefficients, $Ax = \dot x$, with the matrix A having nonnegative off-diagonal elements and zero column sums, occur in compartmental analysis. The steady-state solution leads to the homogeneous system of linear equations $Ax(\infty ) = \dot x(\infty ) = 0$. $LU$-factorization, the Crout algorithm, error analysis and solution of a modified system are treated.