73 research outputs found
Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs
A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK) method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK) methods
High Order Multistep Methods with Improved Phase-Lag Characteristics for the Integration of the Schr\"odinger Equation
In this work we introduce a new family of twelve-step linear multistep
methods for the integration of the Schr\"odinger equation. The new methods are
constructed by adopting a new methodology which improves the phase lag
characteristics by vanishing both the phase lag function and its first
derivatives at a specific frequency. This results in decreasing the sensitivity
of the integration method on the estimated frequency of the problem. The
efficiency of the new family of methods is proved via error analysis and
numerical applications.Comment: 36 pages, 6 figure
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