A practical method to integrate some stiff systems

A compact, absolutely stable numerical method is presented to integrate stiff systems of pseudo-linear, ordinary, first-order differential equations, commonly found in the simulation of biological models. Solutions are stepwise approximated by a complete set of first order rational polynomials. Mass balance is preserved by the approximations. No matrix inversions are required. Besides being stable, the method is also convergent and can be used with deferred approximation to the limit h = 0. Comparisons between this method and the Stoer-Bullirsch algorithm and fourth-order Runge-Kutta method are presented.