A new numerical method for stiff differential equations

Abstract

A new class of multistep methods for stiff ordinary differential equations is presented. The method is based in the application of estimation functions for the derivatives and the state variables, allowing the transformation of the 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, deduced from a combined analysis of stability and convergence order. That is, the estimation function coefficients are recomputed at each time step. The convergence order of the resulting scheme is better than the equivalent linear multistep methods, while preserving the properties of stability.