MULTISTAGE SYMMETRIC TWO-STEP P-STABLE METHOD WITH VANISHED PHASE-LAG AND ITS FIRST, SECOND AND THIRD DERIVATIVES

A new three-stage symmetric two-step P-Stable eight algebraic order method is obtained in the present paper. We will study in this paper the impact of the vanishing of the phase–lag and its first, second and third derivatives of the new obtained multistage twostep method on the efficiency of the method. More specifically we will investigate (1) the development of the new family of methods, (2) its local truncation error (LTE), (3) its stability stability (interval of periodicity) using a scalar test equation with frequency different than the frequency of the scalar test equation used for phase–lag analysis (stability analysis), (4) its effectiveness with application on the coupled differential equations arising from the Schr¨odinger equation.