The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one-dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of gradient symplectic algorithms is particularly suited for solving harmonic-oscillato...

An important goal in astrophysics is to model phenomena such as the gravitational collapse of stars and accretion onto black holes. Under the assumption that the spacetime metric remains fixed on the time scales of fluid motion, the relevant physics can be modeled by the equations of relativistic hydrodynamics. These equations form a system of hyperbolic balance laws that are strongly nonlinear...

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Quasi-periodic responses composed of multiple base frequencies widely exist in science and engineering problems. The harmonic balance (MHB) method is one the most commonly used approaches for such However, it limited by low-order estimations due to complex symbolic operations practical uses. Many variants have been developed improve MHB method, among which time domain MHB-like methods are regar...