American Institute of Mathematical Sciences

Advanced
July  2008, 10(1): 239-263. doi: 10.3934/dcdsb.2008.10.239

A linearly implicit finite difference method for a Klein-Gordon-Schrödinger system modeling electron-ion plasma waves

Pavlos Xanthopoulos 1, and  Georgios E. Zouraris 2,

1. 

Max-Planck-Institut für Plasmaphysik, Teilinstitut Greifswald, Wendelsteinstrasse 1, D-17491 Greifswald, Germany
2. 

Department of Mathematics, University of Crete, GR-714 09 Heraklion, Crete, Greece

Received  January 2007 Revised  September 2007 Published  April 2008

An initial and Dirichlet boundary value-problem for a Klein– Gordon–Schrödinger-type system of equations is considered, which describes the nonlinear interaction between high frequency electron waves and low frequency ion plasma waves in a homogeneous magnetic field. To approximate the solution to the problem a linearly implicit finite difference method is proposed, the convergence of which is ensured by deriving a second order error estimate in a discrete energy norm that is stronger than the discrete maximum norm. The numerical implementation of the method gives a computational confirmation of its order of convergence and recovers known theoretical results for the behavior of the solution, while revealing additional nonlinear features.
Keywords: plasma physics, linearly implicit finite difference method, a priori error estimates..
Mathematics Subject Classification: Primary: 65M12, 65M15, 65M06; Secondary: 82D1.
Citation: Pavlos Xanthopoulos, Georgios E. Zouraris. A linearly implicit finite difference method for a Klein-Gordon-Schrödinger system modeling electron-ion plasma waves. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 239-263. doi: 10.3934/dcdsb.2008.10.239
[1]

Weizhu Bao, Chunmei Su. Uniform error estimates of a finite difference method for the Klein-Gordon-Schrödinger system in the nonrelativistic and massless limit regimes. Kinetic & Related Models, 2018, 11 (4) : 1037-1062. doi: 10.3934/krm.2018040
[2]

Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control & Related Fields, 2021, 11 (3) : 601-624. doi: 10.3934/mcrf.2021014
[3]

Liupeng Wang, Yunqing Huang. Error estimates for second-order SAV finite element method to phase field crystal model. Electronic Research Archive, 2021, 29 (1) : 1735-1752. doi: 10.3934/era.2020089
[4]

Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889
[5]

Lijuan Wang, Jun Zou. Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1641-1670. doi: 10.3934/dcdsb.2010.14.1641
[6]

Jie Shen, Xiaofeng Yang. Error estimates for finite element approximations of consistent splitting schemes for incompressible flows. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 663-676. doi: 10.3934/dcdsb.2007.8.663
[7]

Xiaofeng Yang. Error analysis of stabilized semi-implicit method of Allen-Cahn equation. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 1057-1070. doi: 10.3934/dcdsb.2009.11.1057
[8]

Wolf-Jürgen Beyn, Raphael Kruse. Two-sided error estimates for the stochastic theta method. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 389-407. doi: 10.3934/dcdsb.2010.14.389
[9]

Sebastian Bauer. A non-relativistic model of plasma physics containing a radiation reaction term. Kinetic & Related Models, 2018, 11 (1) : 25-42. doi: 10.3934/krm.2018002
[10]

Jessy Mallet, Stéphane Brull, Bruno Dubroca. General moment system for plasma physics based on minimum entropy principle. Kinetic & Related Models, 2015, 8 (3) : 533-558. doi: 10.3934/krm.2015.8.533
[11]

Baptiste Fedele, Claudia Negulescu. Numerical study of an anisotropic Vlasov equation arising in plasma physics. Kinetic & Related Models, 2018, 11 (6) : 1395-1426. doi: 10.3934/krm.2018055
[12]

Ovidiu Carja, Victor Postolache. A Priori estimates for solutions of differential inclusions. Conference Publications, 2011, 2011 (Special) : 258-264. doi: 10.3934/proc.2011.2011.258
[13]

Hongsong Feng, Shan Zhao. A multigrid based finite difference method for solving parabolic interface problem. Electronic Research Archive, , () : -. doi: 10.3934/era.2021031
[14]

Junxiang Li, Yan Gao, Tao Dai, Chunming Ye, Qiang Su, Jiazhen Huo. Substitution secant/finite difference method to large sparse minimax problems. Journal of Industrial & Management Optimization, 2014, 10 (2) : 637-663. doi: 10.3934/jimo.2014.10.637
[15]

Xufeng Xiao, Xinlong Feng, Jinyun Yuan. The stabilized semi-implicit finite element method for the surface Allen-Cahn equation. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2857-2877. doi: 10.3934/dcdsb.2017154
[16]

Dominik Hafemeyer, Florian Mannel, Ira Neitzel, Boris Vexler. Finite element error estimates for one-dimensional elliptic optimal control by BV-functions. Mathematical Control & Related Fields, 2020, 10 (2) : 333-363. doi: 10.3934/mcrf.2019041
[17]

Anouar El Harrak, Hatim Tayeq, Amal Bergam. A posteriori error estimates for a finite volume scheme applied to a nonlinear reaction-diffusion equation in population dynamics. Discrete & Continuous Dynamical Systems - S, 2021, 14 (7) : 2183-2197. doi: 10.3934/dcdss.2021062
[18]

Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 75-109. doi: 10.3934/dcdsb.2010.14.75
[19]

JaEun Ku. Maximum norm error estimates for Div least-squares method for Darcy flows. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1305-1318. doi: 10.3934/dcds.2010.26.1305
[20]

Xavier Cabré, Manel Sanchón, Joel Spruck. A priori estimates for semistable solutions of semilinear elliptic equations. Discrete & Continuous Dynamical Systems, 2016, 36 (2) : 601-609. doi: 10.3934/dcds.2016.36.601

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (49)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences