A generator of families of explicit hybrid methods with minimal phase lag is developed in this paper. The methods of the generator have algebraic order six. The main characteristic of the new methods is that they are dissipative, i.e., they are not symmetric and they have not an interval of periodicity. The generator is of dissipation order eight. Numerical results indicate that these new methods are more efficient than older ones, i.e., the property of the phase lag is more crucial than the nonempty interval of periodicity for the construction of the numerical methods for the numerical solution of the Schrodinger-type equations.
Abstract.This paper analyzes and studies the second order scheme of de Pillis' type, which is used for the solution of a linear system. This study leads to a monoparametric family of second order schemes of the aforementioned type and a method of selecting the optimal one is presented. In addition a number of concluding remarks is made and various applications and examples are given, which effectively show in some cases the superiority of our optimal second order scheme over the fastest first order ones like the SOR and AOR schemes. Many points are also made for the possibility of improving on the convergence rates of the optimal scheme of this paper, which suggest further research in this area.
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