Solution of large compartmental models using numerical transform inversion

Compartmental models of biological or physical systems are often described by a system of “stiff” differential equations. In this paper an algorithm for solving a system with linear coefficients is presented that employs numerical inversion of the Laplace transform of the model equations. The inversion algorithms and Gear's backward differentiation method are compared for two stiff test problems and a differential system governing a 27-compartment model of bile acid transport and metabolism. The inversion algorithm is reliable, requires modest computation time on a desktop computer and provides better accuracy than Gear's method, especially for the extremely stiff example.