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Journal articles on the topic 'Lax-Friedrichs'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Shampine, L. F. "Two-step Lax–Friedrichs method." Applied Mathematics Letters 18, no. 10 (October 2005): 1134–36. http://dx.doi.org/10.1016/j.aml.2004.11.007.

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2

Yu, Simin. "A survey of numerical schemes for transportation equation." E3S Web of Conferences 308 (2021): 01020. http://dx.doi.org/10.1051/e3sconf/202130801020.

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The convection-diffusion equation is a fundamental equation that exists widely. The convection-diffusion equation consists of two processes: diffusion and convection. The convection-diffusion equation can also be called drift-diffusion equaintion. The convection – diffusion equation mainly characterizes natural phenomenon in which physical particles, energy are transferred in a system. The well-known linear transport equation is also one kind of convection-diffusion equation. The transport equation can describe the transport of a scalar field such as material feature, chemical reaction or temperature in an incompressible flow. In this paper, we discuss the famous numerical scheme, Lax-Friedrichs method, for the linear transport equation. The important ingredient of the design of the Lax-Friedrichs Method, namely the choice of the numerical fluxes will be discussed in detail. We give a detailed proof of the L1 stability of the Lax-Friedrichs scheme for the linear transport equation. We also address issues related to the implementation of this numerical scheme.
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3

Breuß, Michael. "The correct use of the Lax–Friedrichs method." ESAIM: Mathematical Modelling and Numerical Analysis 38, no. 3 (May 2004): 519–40. http://dx.doi.org/10.1051/m2an:2004027.

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4

Bodnár, Tomáš, Philippe Fraunié, and Karel Kozel. "MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM." Acta Polytechnica 61, SI (February 10, 2021): 49–58. http://dx.doi.org/10.14311/ap.2021.61.0049.

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This paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified equation to the properties of the considered numerical methods.
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5

Marcati, Pierangelo, and Roberto Natalini. "Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 1 (1995): 115–31. http://dx.doi.org/10.1017/s030821050003078x.

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We investigate the Cauchy problem for a hydrodynamic model for semiconductors. An existence theorem of global weak solutions with large initial data is obtained by using the fractional step Lax—Friedrichs scheme and Godounov scheme.
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6

Dallakyan, Gurgen. "Numerical Simulations for Chemotaxis Models." Biomath Communications 6, no. 1 (May 11, 2019): 16. http://dx.doi.org/10.11145/bmc.2019.04.277.

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In the paper, we study the usage of numerical methods in solution of mathematical models of biological problems. More specifically, Keller-Segel type chemotaxis models are discussed, their numerical solutions by sweep and Lax-Friedrichs methods are obtained and interpreted biologically.
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7

Soga, Kohei. "Stochastic and variational approach to the Lax-Friedrichs scheme." Mathematics of Computation 84, no. 292 (July 22, 2014): 629–51. http://dx.doi.org/10.1090/s0025-5718-2014-02863-9.

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8

Kao, Chiu Yen, Stanley Osher, and Jianliang Qian. "Lax–Friedrichs sweeping scheme for static Hamilton–Jacobi equations." Journal of Computational Physics 196, no. 1 (May 2004): 367–91. http://dx.doi.org/10.1016/j.jcp.2003.11.007.

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9

JOVANOVIC, V. "Error Estimates For The Lax — Friedrichs Scheme For Balance Laws." Computational Methods in Applied Mathematics 8, no. 2 (2008): 130–42. http://dx.doi.org/10.2478/cmam-2008-0009.

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AbstractWe first derive the general error estimate for one – dimensional balance laws and afterwards we apply it to the elastodynamics system with source and to the isentropic Euler system with damping.
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10

Baiti, Paolo, Alberto Bressan, and Helge Kristian Jenssen. "Instability of travelling wave profiles for the Lax-Friedrichs scheme." Discrete & Continuous Dynamical Systems - A 13, no. 4 (2005): 877–99. http://dx.doi.org/10.3934/dcds.2005.13.877.

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11

Godillon, Pauline. "Green's function pointwise estimates for the modified Lax–Friedrichs scheme." ESAIM: Mathematical Modelling and Numerical Analysis 37, no. 1 (January 2003): 1–39. http://dx.doi.org/10.1051/m2an:2003022.

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12

Boukadida, T., and A. Y. LeRoux. "A new version of the two-dimensional Lax-Friedrichs scheme." Mathematics of Computation 63, no. 208 (1994): 541. http://dx.doi.org/10.1090/s0025-5718-1994-1242059-3.

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13

Zhu, Peng, and Shuzi Zhou. "Relaxation Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations." Numerical Algorithms 54, no. 3 (October 6, 2009): 325–42. http://dx.doi.org/10.1007/s11075-009-9337-5.

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14

Dubey, Ritesh Kumar, and Biswarup Biswas. "An Analysis on Induced Numerical Oscillations by Lax-Friedrichs Scheme." Differential Equations and Dynamical Systems 25, no. 2 (July 18, 2016): 151–68. http://dx.doi.org/10.1007/s12591-016-0311-0.

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15

Zolfaghary, Azizi, Mohammad Naghashzadegan, and Vahid Shokri. "The impact of the order of numerical schemes on slug flows modeling." Thermal Science 23, no. 6 Part B (2019): 3855–64. http://dx.doi.org/10.2298/tsci171009320z.

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This paper aims to explore the impact of the order of numerical schemes on the simulation of two-phase slug flow with a two-fluid model initiation. The governing equations of the two-fluid model have been solved by a class of Riemann solver. The numerical schemes applied in this paper involve first-order (Lax-Friedrichs and Rusanov), second-order (Ritchmyer), and high-order (flux-corrected transport or FCT and total variance diminishing or TVD). The results suggest that the TVD and FCT are able to predict the slug initiation with high accuracy compared with experimental results. Lax-Friedrichs and Rusanov are both first-order schemes and have second-order truncation error. This second-order truncation error caused numerical diffusion in the solution field and could not predict the slug initiation with high accuracy in contrast to TVD and FCT schemes. Ritchmyer is a second-order scheme and has third-order truncation error. This third-order truncation error caused dispersive results in the solution field and was not a proper scheme.
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16

Gani, MO, MM Hossain, and LS Andallah. "A finite difference scheme for a fluid dynamic traffic flow model appended with two-point boundary condition." GANIT: Journal of Bangladesh Mathematical Society 31 (April 9, 2012): 43–52. http://dx.doi.org/10.3329/ganit.v31i0.10307.

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A fluid dynamic traffic flow model with a linear velocity-density closure relation is considered. The model reads as a quasi-linear first order hyperbolic partial differential equation (PDE) and in order to incorporate initial and boundary data the PDE is treated as an initial boundary value problem (IBVP). The derivation of a first order explicit finite difference scheme of the IBVP for two-point boundary condition is presented which is analogous to the well known Lax-Friedrichs scheme. The Lax-Friedrichs scheme for our model is not straight-forward to implement and one needs to employ a simultaneous physical constraint and stability condition. Therefore, a mathematical analysis is presented in order to establish the physical constraint and stability condition of the scheme. The finite difference scheme is implemented and the graphical presentation of numerical features of error estimation and rate of convergence is produced. Numerical simulation results verify some well understood qualitative behavior of traffic flow.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10307GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 43-52
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17

Sharma, Deepika, and Kavita Goyal. "Wavelet optimized upwind conservative method for traffic flow problems." International Journal of Modern Physics C 31, no. 06 (June 2020): 2050086. http://dx.doi.org/10.1142/s0129183120500862.

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Numerical schemes, namely, upwind nonconservative, upwind conservative, Lax–Friedrichs, Lax–Wendroff, MacCormack and Godunov are applied and compared on traffic flow problems. The best scheme, namely, upwind conservative is used for wavelet-optimized method using Daubechies wavelet for numerically solving the same traffic flow problems. Numerical results corresponding to the traffic flow problem with the help of wavelet-optimized, adaptive grid, upwind conservative method have been given. Moreover, the run time carried out by the developed technique have been compared to that of run time carried out by finite difference technique. It is observed that, in terms of run time, the proposed method performs better.
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18

Chen, Guiqiang. "CONVERGENCE OF THE LAX–FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (III)." Acta Mathematica Scientia 6, no. 1 (January 1986): 75–120. http://dx.doi.org/10.1016/s0252-9602(18)30535-6.

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19

Ding, Xiaxi, Guiqiang Chen, and Peizhu Luo. "CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (I)." Acta Mathematica Scientia 5, no. 4 (October 1985): 415–32. http://dx.doi.org/10.1016/s0252-9602(18)30542-3.

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20

Ding, Xiaxi, Guiqiang Chen, and Peizhu Luo. "CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (II)." Acta Mathematica Scientia 5, no. 4 (October 1985): 433–72. http://dx.doi.org/10.1016/s0252-9602(18)30543-5.

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21

Soga, Kohei. "More on stochastic and variational approach to the Lax-Friedrichs scheme." Mathematics of Computation 85, no. 301 (February 10, 2016): 2161–93. http://dx.doi.org/10.1090/mcom/3061.

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22

Küther, Marc. "Error Estimates for the Staggered Lax--Friedrichs Scheme on Unstructured Grids." SIAM Journal on Numerical Analysis 39, no. 4 (January 2001): 1269–301. http://dx.doi.org/10.1137/s0036142900374275.

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23

Chatterjee, N., and U. S. Fjordholm. "A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws." IMA Journal of Numerical Analysis 40, no. 1 (November 9, 2018): 405–21. http://dx.doi.org/10.1093/imanum/dry074.

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Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.
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24

Chiarello, Felisia Angela, and Paola Goatin. "Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 1 (January 2018): 163–80. http://dx.doi.org/10.1051/m2an/2017066.

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We prove the well-posedness of entropy weak solutions for a class of scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem by a Lax-Friedrichs scheme and we provide L∞ and BV estimates for the sequence of approximate solutions. Stability with respect to the initial data is obtained from the entropy condition through the doubling of variable technique. The limit model as the kernel support tends to infinity is also studied.
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25

Arry Sanjoyo, Bandung, Mochamad Hariadi, and Mauridhi Hery Purnomo. "Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water." EMITTER International Journal of Engineering Technology 8, no. 1 (June 2, 2020): 19–34. http://dx.doi.org/10.24003/emitter.v8i1.479.

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Many game applications require fluid flow visualization of shallow water, especially dam-break flow. A Shallow Water Equation (SWE) is a mathematical model of shallow water flow which can be used to compute the flow depth and velocity. We propose a stable algorithm for visualization of dam-break flow on flat and flat with bumps topography. We choose Lax-Friedrichs scheme as the numerical method for solving the SWE. Then, we investigate the consistency, stability, and convergence of the scheme. Finally, we transform the strategy into a visualization algorithm of SWE and analyze the complexity. The results of this paper are: 1) the Lax-Friedrichs scheme that is consistent and conditionally stable; furthermore, if the stability condition is satisfied, the scheme is convergent; 2) an algorithm to visualize flow depth and velocity which has complexity O(N) in each time iteration. We have applied the algorithm to flat and flat with bumps topography. According to visualization results, the numerical solution is very close to analytical solution in the case of flat topography. In the case of flat with bumps topography, the algorithm can visualize the dam-break flow and after a long time the numerical solution is very close to the analytical steady-state solution. Hence the proposed visualization algorithm is suitable for game applications containing flat with bumps environments.
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26

Frid, Hermano. "Invariant regions under Lax-Friedrichs scheme for multidimensional systems of conservation laws." Discrete & Continuous Dynamical Systems - A 1, no. 4 (1995): 585–93. http://dx.doi.org/10.3934/dcds.1995.1.585.

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27

Yang, Tong, and Huijiang Zhao †. "BV Estimates on Lax–Friedrichs' Scheme or a Model of Radiating Gas." Applicable Analysis 83, no. 5 (May 2004): 533–39. http://dx.doi.org/10.1080/00036810410001649674.

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28

Zhang, Jing, and Changjiang Zhu. "BV-estimates of Lax-Friedrichs' scheme for hyperbolic conservation laws with relaxation." Mathematical Methods in the Applied Sciences 31, no. 8 (September 13, 2007): 959–74. http://dx.doi.org/10.1002/mma.954.

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29

Rider, W. J., and R. B. Lowrie. "The use of classical Lax-Friedrichs Riemann solvers with discontinuous Galerkin methods." International Journal for Numerical Methods in Fluids 40, no. 3-4 (2002): 479–86. http://dx.doi.org/10.1002/fld.334.

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30

CHEN, GUI-QIANG, and ELEUTERIO F. TORO. "CENTERED DIFFERENCE SCHEMES FOR NONLINEAR HYPERBOLIC EQUATIONS." Journal of Hyperbolic Differential Equations 01, no. 03 (September 2004): 531–66. http://dx.doi.org/10.1142/s0219891604000202.

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A hierarchy of centered (non-upwind) difference schemes is identified for solving hyperbolic equations. The bottom of the hierarchy is the classical Lax–Friedrichs scheme, which is the least accurate in computation, and the top of the hierarchy is the FORCE scheme, which is the optimal scheme in the family. The FORCE scheme is optimal in the sense that it is monotone, has the optimal stability condition for explicit methods, and has the smallest numerical viscosity. It is shown that the FORCE scheme is consistent with the Lax entropy inequality, that is, the limit functions of the FORCE approximate solutions are entropy solutions. The convergence of the FORCE scheme is also established for the isentropic Euler equations and the shallow water equations. Some related centered difference schemes are also surveyed and discussed.
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31

Liska, Richard, Mikhail Shashkov, and Burton Wendroff. "The early influence of peter lax on computational hydrodynamics and an application of lax-friedrichs and lax-wendroff on triangular grids in lagrangian coordinates." Acta Mathematica Scientia 31, no. 6 (November 2011): 2195–202. http://dx.doi.org/10.1016/s0252-9602(11)60393-7.

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32

Coelho, R. M. L., P. L. C. Lage, and A. Silva Telles. "A comparison of hyperbolic solvers II: ausm-type and Hybrid Lax-Wendroff-Lax-Friedrichs methods for two-phase flows." Brazilian Journal of Chemical Engineering 27, no. 1 (March 2010): 153–71. http://dx.doi.org/10.1590/s0104-66322010000100014.

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33

Araujo, Isamara L. N., Panters Rodríguez-Bermúdez, and Yoisell Rodríguez-Núñez. "Numerical Study for Two-Phase Flow with Gravity in Homogeneous and Piecewise-Homogeneous Porous Media." TEMA (São Carlos) 21, no. 1 (March 27, 2020): 21. http://dx.doi.org/10.5540/tema.2020.021.01.21.

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In this work we study two-phase flow with gravity either in 1-rock homogeneous media or 2-rocks composed media, this phenomenon can be modeled by a non-linear scalar conservation law with continuous flux function or discontinuous flux function, respectively. Our study is essentially from a numerical point of view, we apply the new Lagrangian-Eulerian finite difference method developed by Abreu and Pérez and the Lax-Friedrichs classic method to obtain numerical entropic solutions. Comparisons between numerical and analytical solutions show the efficiency of the methods even for discontinuous flux function.
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34

Yun WU, and Haixin JIANG. "Local Oscillations in Generalized Lax-Friedrichs Schemes for Linear Advection Equation with Damping." Journal of Convergence Information Technology 7, no. 22 (December 31, 2012): 306–14. http://dx.doi.org/10.4156/jcit.vol7.issue22.36.

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35

Cao, Wentao, Feimin Huang, and Dehua Wang. "Isometric Immersion of Surface with Negative Gauss Curvature and the Lax--Friedrichs Scheme." SIAM Journal on Mathematical Analysis 48, no. 3 (January 2016): 2227–49. http://dx.doi.org/10.1137/15m1041766.

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36

Chen, Weitao, Ching-Shan Chou, and Chiu-Yen Kao. "Lax–Friedrichs fast sweeping methods for steady state problems for hyperbolic conservation laws." Journal of Computational Physics 234 (February 2013): 452–71. http://dx.doi.org/10.1016/j.jcp.2012.10.008.

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37

Li, Tian-Hong. "Convergence of the Lax–Friedrichs scheme for isothermal gas dynamics with semiconductor devices." Zeitschrift für angewandte Mathematik und Physik 57, no. 1 (November 2005): 12–32. http://dx.doi.org/10.1007/s00033-005-0001-1.

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38

Breuß, Michael. "About the Lax-Friedrichs scheme for the numerical approximation of hyperbolic conservation laws." PAMM 4, no. 1 (December 2004): 636–37. http://dx.doi.org/10.1002/pamm.200410299.

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39

Rossi, Elena, Jennifer Weißen, Paola Goatin, and Simone Göttlich. "Well-posedness of a non-local model for material flow on conveyor belts." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 2 (March 2020): 679–704. http://dx.doi.org/10.1051/m2an/2019062.

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In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensional splitting, we prove the convergence of the approximate solutions, where the main difficulty arises in the treatment of the discontinuity occurring in the flux function. In particular, we compare a Roe-type scheme to the well-established Lax–Friedrichs method and provide a numerical study highlighting the benefits of the Roe discretisation. Besides, we also prove the L1-Lipschitz continuous dependence on the initial datum, ensuring the uniqueness of the solution.
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40

D. Towers, John. "The Lax-Friedrichs scheme for interaction between the inviscid Burgers equation and multiple particles." Networks & Heterogeneous Media 15, no. 1 (2020): 143–69. http://dx.doi.org/10.3934/nhm.2020007.

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41

Kao, Chiu Yen, Carmeliza Navasca, and Stanley Osher. "The Lax–Friedrichs sweeping method for optimal control problems in continuous and hybrid dynamics." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): e1561-e1572. http://dx.doi.org/10.1016/j.na.2005.01.061.

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42

Setiyowati, R., and Sumardi. "A Simulation of Shallow Water Wave Equation Using Finite Volume Method: Lax-Friedrichs Scheme." Journal of Physics: Conference Series 1306 (August 2019): 012022. http://dx.doi.org/10.1088/1742-6596/1306/1/012022.

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43

Li, Jia, Dazhi Zhang, Xiong Meng, Boying Wu, and Qiang Zhang. "Discontinuous Galerkin Methods for Nonlinear Scalar Conservation Laws: Generalized Local Lax--Friedrichs Numerical Fluxes." SIAM Journal on Numerical Analysis 58, no. 1 (January 2020): 1–20. http://dx.doi.org/10.1137/19m1243798.

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44

Wang, Dean, and Tseelmaa Byambaakhuu. "High-Order Lax-Friedrichs WENO Fast Sweeping Methods for the SN Neutron Transport Equation." Nuclear Science and Engineering 193, no. 9 (March 25, 2019): 982–90. http://dx.doi.org/10.1080/00295639.2019.1582316.

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45

Yang, Tong, Huijiang Zhao, and Changjiang Zhu. "BV estimates of Lax-Friedrichs’ scheme for a class of nonlinear hyperbolic conservation laws." Proceedings of the American Mathematical Society 131, no. 4 (October 1, 2002): 1257–66. http://dx.doi.org/10.1090/s0002-9939-02-06688-1.

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46

Chen, Weitao, Ching-Shan Chou, and Chiu-Yen Kao. "Lax–Friedrichs Multigrid Fast Sweeping Methods for Steady State Problems for Hyperbolic Conservation Laws." Journal of Scientific Computing 64, no. 3 (March 18, 2015): 591–618. http://dx.doi.org/10.1007/s10915-015-0006-7.

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47

sun, Xia, Guodong Wang, and Yanying Ma. "A new modified Local Lax–Friedrichs scheme for scalar conservation laws with discontinuous flux." Applied Mathematics Letters 105 (July 2020): 106328. http://dx.doi.org/10.1016/j.aml.2020.106328.

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48

Kabir, MH, and LS Andallah. "Numerical Solution of a Multilane Traffic Flow Model." GANIT: Journal of Bangladesh Mathematical Society 33 (January 13, 2014): 25–32. http://dx.doi.org/10.3329/ganit.v33i0.17653.

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This paper performs the numerical solution of a macroscopic multilane traffic flow model based on a linear density-velocity relationship. A multilane traffic flow is modeled by a system of nonlinear partial differential equation appended with initial and boundary conditions reads as an initial boundary value problem (IBVP). We present numerical simulation of the IBVP by a finite difference scheme named Lax-Friedrichs scheme and report on the stability and efficiency of the scheme by performing numerical experiments. The computed result satisfies some well known qualitative features of the solution. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 25-32 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17653
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49

Vasquéz, Yolanda Maria, and Dr José Javier Laguardia. "Estudio del Flujo Vehicular Mediante un Modelo de Lighthill-Whitham-Richards." KnE Engineering 3, no. 1 (February 11, 2018): 449. http://dx.doi.org/10.18502/keg.v3i1.1449.

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El tránsito vehicular tanto en carreteras como en redes urbanas ha representado un problema a resolver desde el segundo cuarto del siglo pasado debido al aumento del número de usuarios. Por esto, resulta sumamente importante crear modelos que permitan entender los fenómenos de tráfico.En este artículo se presenta como establecer un modelo macroscópico del flujo vehicular para simular el tráfico de forma que se disponga de una herramienta para la toma de decisiones. Finalmente se muestran los resultados obtenidos al aplicar el modelo sobre un caso de estudio como es el problema del semáforo.Palabras claves: Flujo vehicular, Modelo Macroscópico, Esquema de Lax-Friedrichs, Simulación Numérica
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50

Petaccia, Gabriella, Luigi Natale, Fabrizio Savi, Mirjana Velickovic, Yves Zech, and Sandra Soares-Frazão. "Flood wave propagation in steep mountain rivers." Journal of Hydroinformatics 15, no. 1 (July 12, 2012): 120–37. http://dx.doi.org/10.2166/hydro.2012.122.

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Most of the recent developments concerning efficient numerical schemes to solve the shallow-water equations in view of real world flood modelling purposes concern the two-dimensional form of the equations or the one-dimensional form written for rectangular, unit-width channels. Extension of these efficient schemes to the one-dimensional cross-sectional averaged shallow-water equations is not straightforward, especially when complex natural topographies are considered. This paper presents different formulations of numerical schemes based on the HLL (Harten–Lax–van Leer) solver, and the adaptation of the topographical source term treatment when cross-sections of arbitrary shape are considered. Coupled and uncoupled formulations of the equations are considered, in combination with centred and lateralised source term treatment. These schemes are compared to a numerical solver of Lax Friedrichs type based on a staggered grid. The proposed schemes are first tested against two theoretical benchmark tests and then applied to the Brembo River, an Italian alpine river, firstly simulating a steady-state condition and secondly reproducing the 2002 flood wave propagation.
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