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Oscillatory behavior of AsymptoticPreserving splitting methods for a linear model of diffusive relaxation
1.  Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706, United States 
2.  Computational Physics Group (CCS2) and Center for Nonlinear Studies (TCNLS), Mail Stop B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, United States 
[1] 
Jingwei Hu, Shi Jin, Li Wang. An asymptoticpreserving scheme for the semiconductor Boltzmann equation with twoscale collisions: A splitting approach. Kinetic & Related Models, 2015, 8 (4) : 707723. doi: 10.3934/krm.2015.8.707 
[2] 
Stéphane Brull, Pierre Degond, Fabrice Deluzet, Alexandre Mouton. Asymptoticpreserving scheme for a bifluid EulerLorentz model. Kinetic & Related Models, 2011, 4 (4) : 9911023. doi: 10.3934/krm.2011.4.991 
[3] 
Alina Chertock, Changhui Tan, Bokai Yan. An asymptotic preserving scheme for kinetic models with singular limit. Kinetic & Related Models, 2018, 11 (4) : 735756. doi: 10.3934/krm.2018030 
[4] 
Alina Chertock, Alexander Kurganov, Mária LukáčováMedvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195216. doi: 10.3934/krm.2019009 
[5] 
Nicolas Crouseilles, Mohammed Lemou, SV Raghurama Rao, Ankit Ruhi, Muddu Sekhar. Asymptotic preserving scheme for a kinetic model describing incompressible fluids. Kinetic & Related Models, 2016, 9 (1) : 5174. doi: 10.3934/krm.2016.9.51 
[6] 
Manh Hong Duong, Yulong Lu. An operator splitting scheme for the fractional kinetic FokkerPlanck equation. Discrete & Continuous Dynamical Systems  A, 2019, 39 (10) : 57075727. doi: 10.3934/dcds.2019250 
[7] 
Dominika Pilarczyk. Asymptotic stability of singular solution to nonlinear heat equation. Discrete & Continuous Dynamical Systems  A, 2009, 25 (3) : 9911001. doi: 10.3934/dcds.2009.25.991 
[8] 
Donatella Donatelli, Corrado Lattanzio. On the diffusive stress relaxation for multidimensional viscoelasticity. Communications on Pure & Applied Analysis, 2009, 8 (2) : 645654. doi: 10.3934/cpaa.2009.8.645 
[9] 
Andreas C. Aristotelous, Ohannes Karakashian, Steven M. Wise. A mixed discontinuous Galerkin, convex splitting scheme for a modified CahnHilliard equation and an efficient nonlinear multigrid solver. Discrete & Continuous Dynamical Systems  B, 2013, 18 (9) : 22112238. doi: 10.3934/dcdsb.2013.18.2211 
[10] 
Constantine M. Dafermos. Hyperbolic balance laws with relaxation. Discrete & Continuous Dynamical Systems  A, 2016, 36 (8) : 42714285. doi: 10.3934/dcds.2016.36.4271 
[11] 
Tetsuya Ishiwata, Kota Kumazaki. Structure preserving finite difference scheme for the LandauLifshitz equation with applied magnetic field. Conference Publications, 2015, 2015 (special) : 644651. doi: 10.3934/proc.2015.0644 
[12] 
Nicolas Crouseilles, Mohammed Lemou. An asymptotic preserving scheme based on a micromacro decomposition for Collisional Vlasov equations: diffusion and highfield scaling limits. Kinetic & Related Models, 2011, 4 (2) : 441477. doi: 10.3934/krm.2011.4.441 
[13] 
Vladimir V. Chepyzhov, Anna Kostianko, Sergey Zelik. Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (3) : 11151142. doi: 10.3934/dcdsb.2019009 
[14] 
Johannes Eilinghoff, Roland Schnaubelt. Error analysis of an ADI splitting scheme for the inhomogeneous Maxwell equations. Discrete & Continuous Dynamical Systems  A, 2018, 38 (11) : 56855709. doi: 10.3934/dcds.2018248 
[15] 
Roland Zweimüller. Asymptotic orbit complexity of infinite measure preserving transformations. Discrete & Continuous Dynamical Systems  A, 2006, 15 (1) : 353366. doi: 10.3934/dcds.2006.15.353 
[16] 
Luis Caffarelli, Fanghua Lin. Nonlocal heat flows preserving the L^{2} energy. Discrete & Continuous Dynamical Systems  A, 2009, 23 (1&2) : 4964. doi: 10.3934/dcds.2009.23.49 
[17] 
Sandra Carillo. Some remarks on the model of rigid heat conductor with memory: Unbounded heat relaxation function. Evolution Equations & Control Theory, 2019, 8 (1) : 3142. doi: 10.3934/eect.2019002 
[18] 
Petra Csomós, Hermann Mena. Fouriersplitting method for solving hyperbolic LQR problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 1746. doi: 10.3934/naco.2018002 
[19] 
WenQing Xu. Boundary conditions for multidimensional hyperbolic relaxation problems. Conference Publications, 2003, 2003 (Special) : 916925. doi: 10.3934/proc.2003.2003.916 
[20] 
Ali Unver, Christian Ringhofer, Dieter Armbruster. A hyperbolic relaxation model for product flow in complex production networks. Conference Publications, 2009, 2009 (Special) : 790799. doi: 10.3934/proc.2009.2009.790 
2018 Impact Factor: 1.38
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