Solving stiff differential equations in the simulation of physical systems

Abstract

Computer simulation of dynamic systems often requires the solution of a set of stiff ordinary differential equations. The solution involves the eigenvalues of the Jacobian matrix. The greater the spread in eigenvalues, the more time-consuming the solutions become if one uses standard numerical techniques. In many cases, the differential equations are so stiff that accurate numerical solutions are unecon omic. In this paper we propose new techniques for solving stiff differential equations. These algo rithms are based on implicit Runge-Kutta procedures with complete error estimates. Experiments show that the new techniques are superior to Gear's method for solving mathematical models for real sys tems in chemical engineering, biology, and laser kinetics.