The optimal trajectory planning problem for multiple trains under fixed block signaling systems and moving block signaling systems is considered. Two approaches are proposed to solve this optimal control problem for multiple trains: the greedy approach and the simultaneous approach. In each solution approach, the trajectory planning problem is transformed into a mixed integer linear programming...

The numerical approximation of the solution of the time-dependent Schrödinger equation arising in ultrafast laser dynamics is discussed. The linear Schrödinger equation is reduced to a computationally tractable, lower dimensional system of nonlinear partial differential equations by the multi-configuration time-dependent Hartree-Fock method. This method serves to approximate the original wave f...

this research focuses on proposing an optimal trajectory planning and control method of two link rigid-flexible manipulators (tlrfm) for dynamic object manipulation (dom) missions. for the first time, achievement of dom task using a rotating one flexible link robot was taken into account in [20]. the authors do not aim to contribute on either trajectory tracking or vibration control of the end-...

In this paper, a linear Chebyshev pseudospectral method (LCPM) is proposed to solve the nonlinear optimal control problems (OCPs) with hard terminal constraints and unspecified final time, which uses collocation scheme quasi-linearization. First, Taylor expansion around differential equations of system used obtain set perturbation equations. Second, first-order necessary conditions for OCPs the...

We solve the time-dependent Schrödinger equation for molecular dynamics using a pseudospectral method with global, exponentially decaying, Hagedorn basis functions. The approximation properties of the Hagedorn basis depend strongly on the scaling of the spatial coordinates. Using results from control theory we develop a time-dependent scaling which adaptively matches the basis to the wave packe...

Seismic modeling is a foundation of geophysical date processing. A multisymplectic pseudospectral method for seismic modeling is presented in this paper. This method takes the multisymplectic structure of the scalar wave equation into account and possesses discrete multisymplectic conservation laws. Numerical experiments demonstrate the remarkable capability of this new method for long-time sim...

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.

An efficient and accurate exponential wave integrator Fourier pseudospectral (EWI-FP) method is proposed and analyzed for solving the symmetric regularized-long-wave (SRLW) equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseu...

Epilepsy is a neurological disorder in which patients have recurrent seizures. Seizures occur in conjunction with abnormal electrical brain activity which can be recorded by the electroencephalogram (EEG). Often, this abnormal brain activity consists of high amplitude regular spike-wave oscillations as opposed to low amplitude irregular oscillations in the non-seizure state. Active brain stimul...