Solution of Homogeneous Systems of Linear Equations Arising from Compartmental Models

摘要

Systems of linear differential equations with constant coefficients, Ax = x-dot, 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(infinity) = x-dot(infinity) = 0. LU factorization, the Crout algorithm, error analysis, and solution of a modified system are treated. 3 figures. (ERA citation 06:005629)