Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations

Abstract

In the numerical solution of large stiff systems of ordinary differential equations, matrix operations associated with the solution of linear equations often dominate the solution time. A matrix factorization is suggested that will allow efficient updating after a change in stepsize or order. This updating technique is shown to be applicable to a wide variety of methods for stiff systems including multistep methods, Runge-Kutta methods, and methods using a rational function of a matrix The technique is particularly useful if the system is large and the Jacobian is dense Numerical results are included to illustrate the use of the technique.