NEW CLASS OF MULTISTEP METHODS WITH ADAPTIVE COEFFICIENTS

G BORONI; P LOTITO; A CLAUSSE

Encuentro; ENIEF; 2007

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.