scholarly journals A flexible symplectic scheme for two-dimensional Schrödinger equation with highly accurate RBFS quasi-interpolation

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5451-5461 ◽  
Author(s):  
Shengliang Zhang ◽  
Liping Zhang
Keyword(s):  
Numerical Experiments ◽  
Time Integration ◽  
Time Dependent ◽  
High Order Accuracy ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Order Accuracy ◽  
Symplectic Scheme ◽  
Long Time ◽  
Long Time Integration

Based on highly accurate multiquadric quasi-interpolation, this study suggests a meshless symplectic procedure for two-dimensional time-dependent Schr?dinger equation. The method is highorder accurate, flexible with respect to the geometry, computationally efficient and easy to implement. We also present a theoretical framework to show the conservativeness and convergence of the proposed method. As the numerical experiments show, it not only offers a high order accuracy but also has a good performance in the long time integration.

High Order Accuracy Computational Methods for Long Time Integration of Nonlinear PDEs in Complex Domains

1998 ◽  
Author(s):  
David Gottlieb ◽  
C. W. Shu ◽  
P. F. Fischer ◽  
W. S. Don ◽  
J. Hesthaven
Keyword(s):  
Computational Methods ◽  
Time Integration ◽  
High Order ◽  
Nonlinear Pdes ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
Long Time ◽  
Long Time Integration

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

scholarly journals Integrating Semilinear Wave Problems with Time-Dependent Boundary Values Using Arbitrarily High-Order Splitting Methods

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1113
Author(s):  
Isaías Alonso-Mallo ◽  
Ana M. Portillo
Keyword(s):  
Numerical Experiments ◽  
Splitting Method ◽  
Method Of Lines ◽  
Time Integration ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
High Order ◽  
Time Dependent ◽  
Boundary Values ◽  
Lipschitz Continuous

The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrarily high-order splitting scheme. We propose a technique to incorporate the boundary values that is more accurate than the one obtained in the standard way, which is clearly seen in the numerical experiments. We prove the consistency and convergence, with the same order of the splitting method, of the full discretization carried out with this technique. Although we performed mathematical analysis under the hypothesis that the source term was Lipschitz-continuous, numerical experiments show that this technique works in more general cases.

scholarly journals Clutter Cancellation and Long Time Integration for GNSS-Based Passive Bistatic Radar

2021 ◽  
Vol 13 (4) ◽  
pp. 701 ◽  
Author(s):  
Binbin Wang ◽  
Hao Cha ◽  
Zibo Zhou ◽  
Bin Tian
Keyword(s):  
Fourier Transform ◽  
Target Detection ◽  
Time Integration ◽  
Detection Performance ◽  
Bistatic Radar ◽  
Detection Range ◽  
Robust Detection ◽  
Coherent Integration ◽  
Long Time ◽  
Long Time Integration

Clutter cancellation and long time integration are two vital steps for global navigation satellite system (GNSS)-based bistatic radar target detection. The former eliminates the influence of direct and multipath signals on the target detection performance, and the latter improves the radar detection range. In this paper, the extensive cancellation algorithm (ECA), which projects the surveillance channel signal in the subspace orthogonal to the clutter subspace, is first applied in GNSS-based bistatic radar. As a result, the clutter has been removed from the surveillance channel effectively. For long time integration, a modified version of the Fourier transform (FT), called long-time integration Fourier transform (LIFT), is proposed to obtain a high coherent processing gain. Relative acceleration (RA) is defined to describe the Doppler variation results from the motion of the target and long integration time. With the estimated RA, the Doppler frequency shift compensation is carried out in the LIFT. This method achieves a better and robust detection performance when comparing with the traditional coherent integration method. The simulation results demonstrate the effectiveness and advantages of the proposed processing method.

A method for long-time integration of Lyapunov exponent and vectors along fluid particle trajectories

2021 ◽  
Vol 33 (12) ◽  
pp. 125107
Author(s):  
Zhiwen Cui ◽  
Lihao Zhao
Keyword(s):  
Lyapunov Exponent ◽  
Time Integration ◽  
Fluid Particle ◽  
Particle Trajectories ◽  
Long Time ◽  
Long Time Integration

A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation

1999 ◽  
Vol 123 (1-3) ◽  
pp. 1-6 ◽  
Author(s):  
I.V. Puzynin ◽  
A.V. Selin ◽  
S.I. Vinitsky
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
High Order ◽  
Time Dependent ◽  
High Order Accuracy ◽  
Order Accuracy

scholarly journals New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
T. E. Simos
Keyword(s):  
Time Integration ◽  
Differential Method ◽  
Algebraic Order ◽  
Long Time ◽  
Long Time Integration ◽  
Differential Methods

The closed Newton-Cotes differential methods of high algebraic order for small number of function evaluations are unstable. In this work, we propose a new closed Newton-Cotes trigonometrically fitted differential method of high algebraic order which gives much more efficient results than the well-know ones.

Review on critical technology development of avian radar system

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Weishi Chen ◽  
Yifeng Huang ◽  
Xianfeng Lu ◽  
Jie Zhang
Keyword(s):  
Technology Development ◽  
Time Integration ◽  
Radar System ◽  
Content Type ◽  
Advantages And Disadvantages ◽  
Detection And Tracking ◽  
Critical Technology ◽  
Long Time ◽  
Long Time Integration ◽  
Target Characteristics

Purpose This paper aims to review the critical technology development of avian radar system at airports. Design/methodology/approach After the origin of avian radar technology is discussed, the target characteristics of flying birds are analyzed, including the target echo amplitude, flight speed, flight height, trajectory and micro-Doppler. Four typical airport avian radar systems of Merlin, Accipiter, Robin and CAST are introduced. The performance of different modules such as antenna, target detection and tracking, target recognition and classification, analysis of bird information together determines the detection ability of avian radar. The performances and key technologies of the ubiquitous avian radar are summarized and compared with other systems, and their applications, deployment modes, as well as their advantages and disadvantages are introduced and analyzed. Findings The ubiquitous avian radar achieves the long-time integration of target echoes, which greatly improves detection and classification ability of the targets of birds or drones, even under strong background clutter at airport. In addition, based on the big data of bird situation accumulated by avian radar, the rules of bird activity around the airport can be mined to guide the bird avoidance work. Originality/value This paper presented a novel avian radar system based on ubiquitous digital radar technology. The authors’ experience has confirmed that this system can be effective for airport bird strike prevention and management. In the future, the avian radar system will see continued improvement in both software and hardware, as the system is designed to be easily extensible.

Long Time Integration of the Moon’s Orbit

1982 ◽  
pp. 67-91 ◽  
Author(s):  
F. Mignard
Keyword(s):  
Time Integration ◽  
Long Time ◽  
Long Time Integration

scholarly journals Variational Integrators in Holonomic Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1358
Author(s):  
Shumin Man ◽  
Qiang Gao ◽  
Wanxie Zhong
Keyword(s):  
Variational Principle ◽  
Dynamic Systems ◽  
Time Integration ◽  
Quadrature Rule ◽  
Quadrature Rules ◽  
Variational Integrators ◽  
Lagrange Polynomials ◽  
Holonomic Constraints ◽  
Long Time ◽  
Long Time Integration

Variational integrators for dynamic systems with holonomic constraints are proposed based on Hamilton’s principle. The variational principle is discretized by approximating the generalized coordinates and Lagrange multipliers by Lagrange polynomials, by approximating the integrals by quadrature rules. Meanwhile, constraint points are defined in order to discrete the holonomic constraints. The functional of the variational principle is divided into two parts, i.e., the action of the unconstrained term and the constrained term and the actions of the unconstrained term and the constrained term are integrated separately using different numerical quadrature rules. The influence of interpolation points, quadrature rule and constraint points on the accuracy of the algorithms is analyzed exhaustively. Properties of the proposed algorithms are investigated using examples. Numerical results show that the proposed algorithms have arbitrary high order, satisfy the holonomic constraints with high precision and provide good performance for long-time integration.

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