A type-insensitive ode code based on second derivative formulas

AbstractSeveral effective codes for the solution of stiff ordinary differential equations (ODEs) are based on second derivative formulas. They are inefficient for non-stiff problems. It is shown how to modify such codes to make them reasonably efficient. The modifications make them more efficient for stiff problems as well. Users do not have the information to determine stiffness reliably. The modified codes recognize the type automatically at each step and respond appropriately. It is a great convenience for a user to have one code efficient regardless of the type