摘要：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.
