Jacobian-Dependent Two-Stage Peer Method for Ordinary Differential Equations

In this paper we derive new explicit two-stage peer methods for the numerical solution of ordinary differential equations by using the technique introduced in [2] for Runge-Kutta methods. This technique allows to re-determine the order conditions of classical methods, obtaining new coefficients values. The coefficients of new methods are no longer constant, but depend on the Jacobian function of the ordinary differential equation. The new methods preserve the order of classical peer methods, and are more accurate and with better stability properties. Numerical tests highlight the advantage of new methods especially for stiff problems.