NEW A-STABLE NUMERICAL METHOD FOR DIFFERENTIAL EQUATIONS

G BORONI; P LOTITO; A CLAUSSE

San Luis

Encuentro; ENIEF; 2008

Universidad Nacional de Cuyo

Stiff problems cause singular computational difficulties because explicit methods cannot solve these problems without rigorous limitations on the step size. To obtain high order A-stable methods, it is traditional to turn to Runge-Kutta methods or to linear multistep methods. A new multistep method is proposed for differential-algebraic equations, based in the application of estimation functions for the derivatives and the state variables, which permits the transformation of the original system into a linear algebraic system with non-linear corrections, using the solutions of the previous steps. The originality introduced is a formula for the estimation function coefficients, which is deduced from a combined analysis of stability and convergence order. Numerical experiments are presented comparing the new method with other classical methods.