NEW CLASS OF MULTISTEP METHODS WITH ADAPTIVE COEFFICIENTS

BORONI G.; LOTITO, P.; CLAUSSE A.

Mecánica Computacional

Año: 2007 vol. 26 p. 635 - 653

1666-6070

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.