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Theoretical optimization of finite difference schemes
1. | Université Pierre et Marie Curie-Paris 6, Institut Jean Le Rond d'Alembert, UMR CNRS 71900, Boîte courrier $n^0$ 162, 4 place Jussieu, 75252 Paris, cedex 05. France |
[1] |
Gianluca Frasca-Caccia, Peter E. Hydon. Locally conservative finite difference schemes for the modified KdV equation. Journal of Computational Dynamics, 2019, 6 (2) : 307-323. doi: 10.3934/jcd.2019015 |
[2] |
Emma Hoarau, Claire david@lmm.jussieu.fr David, Pierre Sagaut, Thiên-Hiêp Lê. Lie group study of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 495-505. doi: 10.3934/proc.2007.2007.495 |
[3] |
Adam M. Oberman. Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 221-238. doi: 10.3934/dcdsb.2008.10.221 |
[4] |
Bernard Ducomet, Alexander Zlotnik, Ilya Zlotnik. On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation. Kinetic and Related Models, 2009, 2 (1) : 151-179. doi: 10.3934/krm.2009.2.151 |
[5] |
Takeshi Fukao, Shuji Yoshikawa, Saori Wada. Structure-preserving finite difference schemes for the Cahn-Hilliard equation with dynamic boundary conditions in the one-dimensional case. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1915-1938. doi: 10.3934/cpaa.2017093 |
[6] |
Roumen Anguelov, Jean M.-S. Lubuma, Meir Shillor. Dynamically consistent nonstandard finite difference schemes for continuous dynamical systems. Conference Publications, 2009, 2009 (Special) : 34-43. doi: 10.3934/proc.2009.2009.34 |
[7] |
Qi Hong, Jialing Wang, Yuezheng Gong. Second-order linear structure-preserving modified finite volume schemes for the regularized long wave equation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6445-6464. doi: 10.3934/dcdsb.2019146 |
[8] |
Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control and Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017 |
[9] |
Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159 |
[10] |
Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control and Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73 |
[11] |
Marcel Braukhoff, Ansgar Jüngel. Entropy-dissipating finite-difference schemes for nonlinear fourth-order parabolic equations. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3335-3355. doi: 10.3934/dcdsb.2020234 |
[12] |
Lih-Ing W. Roeger. Dynamically consistent discrete Lotka-Volterra competition models derived from nonstandard finite-difference schemes. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 415-429. doi: 10.3934/dcdsb.2008.9.415 |
[13] |
Houda Hani, Moez Khenissi. Asymptotic behaviors of solutions for finite difference analogue of the Chipot-Weissler equation. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1421-1445. doi: 10.3934/dcdss.2016057 |
[14] |
Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 1503-1528. doi: 10.3934/era.2020079 |
[15] |
Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013 |
[16] |
Laurent Gosse. Well-balanced schemes using elementary solutions for linear models of the Boltzmann equation in one space dimension. Kinetic and Related Models, 2012, 5 (2) : 283-323. doi: 10.3934/krm.2012.5.283 |
[17] |
Moulay Rchid Sidi Ammi, Ismail Jamiai. Finite difference and Legendre spectral method for a time-fractional diffusion-convection equation for image restoration. Discrete and Continuous Dynamical Systems - S, 2018, 11 (1) : 103-117. doi: 10.3934/dcdss.2018007 |
[18] |
Xiaozhong Yang, Xinlong Liu. Numerical analysis of two new finite difference methods for time-fractional telegraph equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3921-3942. doi: 10.3934/dcdsb.2020269 |
[19] |
Ömer Oruç, Alaattin Esen, Fatih Bulut. A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 533-542. doi: 10.3934/dcdss.2019035 |
[20] |
Tetsuya Ishiwata, Kota Kumazaki. Structure preserving finite difference scheme for the Landau-Lifshitz equation with applied magnetic field. Conference Publications, 2015, 2015 (special) : 644-651. doi: 10.3934/proc.2015.0644 |
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