A five-stages symmetric method with improved phase properties

摘要

In this paper, for the first time in the literature, we introduce a new five-stages symmetric two-step method with improved phase and stability properties. The characteristics of the new non linear two-step method are: (1) it is of symmetric type, (2) it is of two-step finite difference pair, (3) it is of five-stages, (4) it is of twelfth-algebraic order, (5) it has vanished the phase-lag and its first and second derivatives, (6) it has improved stability properties for the general problems, (7) it is a P-stable method since it has an interval of periodicity equal to , (8) for the development of the new scheme, the following approximations are used: (a) an approximation developed on the first layer on the point , (b) an approximation developed on the second layer on the point , (c) an approximation developed on the third layer on the point , (d) an approximation developed on the fourth layer on the point and finally, (e) an approximation developed on the fifth (final) layer on the point . For the new developed method we give a full theoretical analysis (error and stability analysis). The efficiency of the new five-stages symmetric two-step method is examined by applying it on the numerical solution of systems of coupled differential equations arising from the Schrodinger equation.