Abstract
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.
Highlights
IntroductionSenu et al [15] developed two-step optimized hybrid methods of fifth and sixth order for the integration of second-order oscillatory Initial Value Problems (IVPs) based on the existing nonzero dissipative hybrid methods with the requirement of phase-lag, dissipation, or amplification error and the differentiation of the phase-lag relations
Consider the numerical solution of the Initial Value Problems (IVPs) for first-order Ordinary Differential Equations (ODEs) in the form of q = f (t, q), q (t0) = q0, (1)whose solutions show an observable oscillatory or periodical behavior
Whose solutions show an observable oscillatory or periodical behavior. Such problems occur in several fields of applied sciences, for example, circuit simulation, molecular dynamics, orbital mechanics, mechanics, electronics, and astrophysics, which have attracted the concern of a number of researchers
Summary
Senu et al [15] developed two-step optimized hybrid methods of fifth and sixth order for the integration of second-order oscillatory IVPs based on the existing nonzero dissipative hybrid methods with the requirement of phase-lag, dissipation, or amplification error and the differentiation of the phase-lag relations. They found out that the nonzero dissipative hybrid methods are more suitable to be optimized than phase-fitted methods.
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