A new implicit backward mid-point rule for highly-stiff systems of ordinary differential equations

Abstract

A new implicit, L-stable, second-order method for the integration of highly-stiff ODE systems is developed. The new method is based on the general mid-point rule and is shown to be more efficient than the classical implicit mid-point rule when low or intermediate accuracy is desired. The new method, which has second-order accuracy, has better stability characteristics (in terms of damping) than the first-order backward Euler method. In addition, the use of global extrapolation is shown to improve the global accuracy and efficiency of the new method and to offer good conservative global error estimates.