10 papers
A Phase-Fitted Runge-Kutta-Nyström method for the Numerical Solution of Initial Value Problems with Oscillating Solutions
D. F. Papadopoulos, Z. A. Anastassi, T. E. Simos
A new Runge-Kutta-Nyström method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this paper. The new method i…
Zero Dispersion and Zero Dissipation Implicit Runge-Kutta Methods for the Numerical Solution of Oscillating IVPs
N. G. Tselios, Z. A. Anastassi, T. E. Simos
In this paper we present two new methods based on an implicit Runge-Kutta method Gauss which is of algebraic order fourth and has two stages: the first one has zero dispersion and…
High Order Phase Fitted Multistep Integrators for the Schrödinger Equation with Improved Frequency Tolerance
D. S. Vlachos, Z. A. Anastassi, T. E. Simos
In this work we introduce a new family of 14-steps linear multistep methods for the integration of the Schrödinger equation. The new methods are phase fitted but they are designed…
High Order Multistep Methods with Improved Phase-Lag Characteristics for the Integration of the Schrödinger Equation
D. S. Vlachos, Z. A. Anastassi, T. E. Simos
In this work we introduce a new family of twelve-step linear multistep methods for the integration of the Schrödinger equation. The new methods are constructed by adopting a new me…
A New Methodology for the Development of Numerical Methods for the Numerical Solution of the Schrödinger Equation
Z. A. Anastassi, D. S. Vlachos, T. E. Simos
In the present paper we introduce a new methodology for the construction of numerical methods for the approximate solution of the one-dimensional Schrödinger equation. The new meth…
Two Optimized Symmetric Eight-Step Implicit Methods for Initial-Value Problems with Oscillating Solutions
G. A. Panopoulos, Z. A. Anastassi, T. E. Simos
In this paper we present two optimized eight-step symmetric implicit methods with phase-lag order ten and infinite (phase-fitted). The methods are constructed to solve numerically…