New Class Of Multistep Methods With Adaptive Coefficients.

Abstract

A new class of multistep methods for stiff ordinary differential equations is presented. The
method is based in the application of estimation functions not only for the derivatives but also for the
state variables, which permits the transformation of original system in a purely algebraic system using
the solutions of previous steps. From this point of view these methods adopt a semi-implicit scheme.
The novelty introduced is an adaptive formula for the estimation function coefficients, which is deduced
from a combined analysis of stability and convergence order. That is, the estimation function
coefficients are recalculated in each time step. The convergence order of the resulting scheme is better
than the equivalent linear multistep methods, while preserving A-stability. Numerical experiments are
presented comparing the new method with BDF.