An improved reduced basis method to solve nonlinear problems

Many works have established the efficiency of asymptotic numerical methods (direct computation of series, the use of Pade approximants, or the reduced basis technique) to solve nonlinear problems (see [1]). A has been written (see [2]) that the reduced basis technique (Rayleigh-Ritz method) is the m ost efficient in term of step lenght. Nevertheless, as long as a cheaper al gorithm to compute the coefficients of the reduced problem is not found, th e most attractive technique remains the rational fractions. In this work is presented an attempt to reduce this computation time. The method consists in coupling Pade approximants with the reduced basis technique in order to obtain an efficient algorithm.