One-leg formulas for stiff differential equations. [DIFSUB

Abstract

There are several effective codes available for solving stiff ordinary differential equations. However, for certain problems these codes will produce reasonable-looking solutions that are not close to the desired solution. This problem can arise if the formula used is stable for unstable problems and completely ignores increasing components of the solution. Unfortunately, the backward differentiation formulas that are the most widely used stiff formulas suffer from this disadvantage. Linear multistep formulas which are stable in large portions of the right half-plane fail to detect the change in the eigenvalues from large negative values to large positive values unless the step size, h, is extremely small. New one-leg multistep formulas are presented that are generalizations of the backward differentiation formulas and whose regions of instability are potentially infinitely large. 6 figures, 5 tables.