Relevant bibliographies by topics / Crank-Nicholson

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'Crank-Nicholson'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Crank-Nicholson"

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SUN, HONGGUANG, WEN CHEN, CHANGPIN LI, and YANGQUAN CHEN. "FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION." International Journal of Bifurcation and Chaos 22, no. 04 (2012): 1250085. http://dx.doi.org/10.1142/s021812741250085x.

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Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variable-order time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investigates numerical schemes for variable-order time fractional diffusion equations in a finite domain. Three finite difference schemes including the explicit scheme, the implicit scheme and the Crank–Nicholso
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Alvarez, A. "Linearized crank-nicholson scheme for nonlinear dirac equations." Journal of Computational Physics 99, no. 2 (1992): 348–50. http://dx.doi.org/10.1016/0021-9991(92)90214-j.

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Chan, Ken, Philip Sewell, Ana Vukovic, and Trevor Benson. "Oblique Du-Fort Frankel Beam Propagation Method." Advances in OptoElectronics 2011 (September 16, 2011): 1–6. http://dx.doi.org/10.1155/2011/196707.

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The oblique BPM based on the Du-Fort Frankel method is presented. The paper demonstrates the accuracy and the computational improvements of the scheme compared to the oblique BPM based on Crank-Nicholson (CN) scheme.
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Ashyralyev, Allaberen, and Serhat Yilmaz. "Modified Crank–Nicholson difference schemes for ultra-parabolic equations." Computers & Mathematics with Applications 64, no. 8 (2012): 2756–64. http://dx.doi.org/10.1016/j.camwa.2012.08.010.

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BELHOCINE, A., and O. I. ABDULLAH. "COMPARATIVE STUDY OF TWO NUMERICAL METHODS FOR SOLVING THE GRAETZ PROBLEM: THE ORTHOGONAL COLLOCATION AND CRANK-NICHOLSON METHODS." Latin American Applied Research - An international journal 46, no. 2 (2016): 73–79. http://dx.doi.org/10.52292/j.laar.2016.330.

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The present set of themes related to the investigations of heat transfer by convection and the transport phenomenon in a cylindrical pipe in laminar flow, commonly called the Graetz Problem, which is to explore the evolution of the temperature profile for a fluid flow in fully developed laminar flow. A numerical method was developed in this work, for visualization of the temperature profile in the fluid flow, whose strategy of calculation is based on the orthogonal collocation method followed by the finite difference method (Crank-Nicholson method). The calculations were effected through a FOR
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Karatay, Ibrahim, and Nurdane Kale. "A new difference scheme for fractional cable equation and stability analysis." International Journal of Applied Mathematical Research 4, no. 1 (2015): 52. http://dx.doi.org/10.14419/ijamr.v4i1.3875.

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<p>We consider the fractional cable equation. For solution of fractional Cable equation involving Caputo fractional derivative, a new difference scheme is constructed based on Crank Nicholson difference scheme. We prove that the proposed method is unconditionally stable by using spectral stability technique.</p>
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García-Ramiro, B., M. A. Illarramendi, and J. Zubia. "Crank-Nicholson method for rate equations in powder random lasers." Journal of Physics: Conference Series 574 (January 21, 2015): 012077. http://dx.doi.org/10.1088/1742-6596/574/1/012077.

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Huang, Z., G. Pan, and H. K. Pan. "Perfect plane wave injection for Crank–Nicholson time-domain method." IET Microwaves, Antennas & Propagation 4, no. 11 (2010): 1855. http://dx.doi.org/10.1049/iet-map.2009.0315.

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Ashyralyev, A. "On Modified Crank–Nicholson Difference Schemes for Stochastic Parabolic Equation." Numerical Functional Analysis and Optimization 29, no. 3-4 (2008): 268–82. http://dx.doi.org/10.1080/01630560801998138.

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Kurtinaitis, A., and F. Ivanauskas. "Finite Difference Solution Methods for a System of the Nonlinear Schrödinger Equations." Nonlinear Analysis: Modelling and Control 9, no. 3 (2004): 247–58. http://dx.doi.org/10.15388/na.2004.9.3.15156.

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This paper investigates finite difference schemes for solving a system of the nonlinear Schrödinger (NLS) equations. Several types of schemes, including explicit, implicit, Hopscotch-type and Crank-Nicholson-type are defined. Cubic spline interpolation is used for solving time-shifting part of equations. The numerical results of the different solution methods are compared using two analytical invariant properties.
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Dissertations / Theses on the topic "Crank-Nicholson"

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Camphouse, R. Chris. "Modeling and Numerical Approximations of Optical Activity in the Chemical Oxygen-Iodine Laser." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28640.

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The chemical oxygen-iodine laser (COIL) has several important military and industrial applications. The concern of this work is do develop a partial differential equation model describing optical behavior in the COIL. Optical behavior of the COIL has traditionally been investigated via a ray tracing method. Photons are represented as discrete particles, and their behavior is described by the geometry of the system. We develop an optical model wherein photons have a wave description. In order to construct the mathematical model, we utilize the theory of paraxial wave optics and Gaussian be
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Christoffer, Zakrisson. "Effektiva lösningsmetoder för Schrödingerekvationen : En jämförelse." Thesis, Uppsala universitet, Tillämpad beräkningsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-208878.

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In this paper the rate of convergence, speed of execution and symplectic properties of the time-integrators Leap-Frog (LF2), fourth order Runge-Kutta(RK4) and Crank-Nicholson (CN2) have been studied. This was done by solving the one-dimensional model for a particle in a box (Dirichlet-conditions). The results show that RK4 is the fastest in achieving higher tolerances, while CN2 is the fastest in achieving lower tolerances. Fourth order corrections of LF (LF4)and CN (CN4) were also studied, though these showed no improvements overLF2 and CN2. All methods were shown to exhibit symplectic behavi
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Rodenkirchen, Jürgen. "On optimum convergence rates of the Crank-Nicholson scheme to the stokes initial value problem in higher order function spaces using realistic data /." 1995. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=007126411&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Book chapters on the topic "Crank-Nicholson"

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Eroglu, Fatma G., and Songul Kaya Merdan. "An Extrapolated Crank Nicholson VMS-POD Method for Darcy Brinkman Equations." In Nonlinear Systems and Complexity. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37141-8_2.

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Ashyralyev, Allaberen, and Serhat Yilmaz. "Modified Crank-Nicholson Difference Schemes for Ultra Parabolic Equations with Neumann Condition." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-41515-9_18.

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Chen, Jixin, and Danping Yang. "A Crank-Nicholson Domain Decomposition Method for Optimal Control Problem of Parabolic Partial Differential Equation." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93873-8_14.

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Conference papers on the topic "Crank-Nicholson"

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Xie, X., and G. Pan. "On Crank-Nicholson Based 3D FDTD." In 2006 IEEE Antennas and Propagation Society International Symposium. IEEE, 2006. http://dx.doi.org/10.1109/aps.2006.1711443.

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Wu, Feng, Weiya Kong, Yu Zhou, et al. "Crank-Nicholson scheme based wind speed modeling." In 2015 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC). IEEE, 2015. http://dx.doi.org/10.1109/appeec.2015.7380925.

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Varnhorn, W. "A CRANK-NICHOLSON METHOD FOR NON-STATIONARY STOKES FLOW." In Topical Problems of Fluid Mechanics 2016. Institute of Thermomechanics, AS CR, v.v.i., 2016. http://dx.doi.org/10.14311/tpfm.2016.032.

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Dai, Weizhong, and Da Yu Tzou. "An Accurate and Stable Numerical Method for Solving a Micro Heat Transfer Model in a 1D N-Carrier System in Spherical Coordinates." In ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer. ASMEDC, 2009. http://dx.doi.org/10.1115/mnhmt2009-18043.

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We consider the generalized micro heat transfer model in a 1D microsphere with N-carriers and Neumann boundary condition in spherical coordinates, which can be applied to describe non-equilibrium heating in biological cells. An accurate and unconditionally stable Crank-Nicholson type of scheme is presented for solving the generalized model, where a new second-order accurate numerical scheme for the Neumann boundary condition is developed so that the overall truncation error is second-order. The present scheme is then tested by a numerical example. Results show that the numerical solution is mu
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ASHYRALYEV, ALLABEREN, and ALI SIRMA. "A NOTE ON THE MODIFIED CRANK-NICHOLSON DIFFERENCE SCHEMES FOR SCHRÖDINGER EQUATION." In Proceedings of the Conference Satellite to ICM 2006. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812778833_0027.

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Ashyralyev, Allaberen, and Ulker Okur. "Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959717.

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Ashyralyev, Allaberen, and Cagin Arikan. "On R-modified Crank-Nicholson difference schemes for the source identification parabolic-elliptic problem." In FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0042757.

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Formánek, Martin, Martin Váňa, Karel Houfek, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Comparison of the Chebyshev Method and the Generalized Crank-Nicholson Method for time Propagation in Quantum Mechanics." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498565.

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Ashyralyev, Allaberen, and Mesut Urun. "Determination of a control parameter of the r-modified Crank-Nicholson difference scheme for the Schrödinger equation." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959700.

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Ashyralyev, Allaberen, and Yusuf Ya’u Gambo. "r–modified Crank-Nicholson difference schemes for one dimensional nonlinear viscous Burgers’ equation for an incompressible flow." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959714.

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Reports on the topic "Crank-Nicholson"

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Pettit, Chris, and D. Wilson. A physics-informed neural network for sound propagation in the atmospheric boundary layer. Engineer Research and Development Center (U.S.), 2021. http://dx.doi.org/10.21079/11681/41034.

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We describe what we believe is the first effort to develop a physics-informed neural network (PINN) to predict sound propagation through the atmospheric boundary layer. PINN is a recent innovation in the application of deep learning to simulate physics. The motivation is to combine the strengths of data-driven models and physics models, thereby producing a regularized surrogate model using less data than a purely data-driven model. In a PINN, the data-driven loss function is augmented with penalty terms for deviations from the underlying physics, e.g., a governing equation or a boundary condit
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Hart, Carl R., D. Keith Wilson, Chris L. Pettit, and Edward T. Nykaza. Machine-Learning of Long-Range Sound Propagation Through Simulated Atmospheric Turbulence. U.S. Army Engineer Research and Development Center, 2021. http://dx.doi.org/10.21079/11681/41182.

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Conventional numerical methods can capture the inherent variability of long-range outdoor sound propagation. However, computational memory and time requirements are high. In contrast, machine-learning models provide very fast predictions. This comes by learning from experimental observations or surrogate data. Yet, it is unknown what type of surrogate data is most suitable for machine-learning. This study used a Crank-Nicholson parabolic equation (CNPE) for generating the surrogate data. The CNPE input data were sampled by the Latin hypercube technique. Two separate datasets comprised 5000 sam
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