References
- Slattery WL, Doolen GD, DeWitt HE. Improved equation of state for the classical one-component plasma. Phys Rev A. 1980;21:2087.
- Hansen JP, Baus M Statistical mechanics of simple coulomb systems. Vol. 59 of Physics Reports. Amsterdam: North-Holland Publishing Company; 1980.
- Liu C, Xu K. A unified gas kinetic scheme for continuum and rarefied flows v: multi- scale and multi-component plasma transport. Commun Comput Phys. 2017;22:1175–1223.
- Igitkhanov Y. Modelling of multi-component plasma for tokes. KIT Scientific Report Nr.7564. Karlsruhe: KIT Scientific Publishing; 2011.
- Zhdanov VM. Transport processes in multicomponent plasma. Plasma Phys Control Fusion. 2002;44:2283.
- Lu D, Li Z, Sang H, et al. Delicate scale multipeak and flat-top structures of solitary waves in multi-component plasmas. Plasma Sci Technol. 2017;19:035002.
- Valentini HB, Herrmann F. Boundary value problems for multi-component plasmas and a generalized bohm criterion. J Phys D Appl Phys. 1996;29:1175–1180.
- Kovtun YV, Skibenko AI, Skibenko EI, et al. Study of multicomponent plasma parameters in the pulsed reflex discharge. Ukrainian J Phys. 2010;55(12):1269–1277.
- Benbelgacem K, Douis S, Meftah M, et al. Effect of electron-ion coupling on the electric microfield distribution in plasmas. Contrib Plasma Phys. 2017;57:176–181.
- Tokar MZ. Approaches to modeling of plasmas containing impurity at arbitrary concentration. Plasma Phys Control Fusion. 2016;58:025015.
- Tokar MZ, Ding R, Koltunov M. Modelling of plasma behaviour in the vicinity of intensive impurity sources. Plasma Phys Control Fusion. 2010;52:075003.
- Tokar MZ. Plasma behaviour near strong sources of impurities. Contrib Plasma Phys. 1996;36:250–254.
- Hansen JP, McDonald IR. Theory of simple liquids. USA: Academic Press; 1976.
- Weiss P. L’hypothèse du champ moléculaire et la propriété ferromagnétique. J Phys Theor Appl. 1907;6(1):661.
- Kelbg G. Theorie des quanten-plasmas. Ann Phys Lpz. 1963;467:219–224.
- Deutsch C. Nodal expansion in a real matter plasma. Phys Lett A. 1977;60:317.
- Deutsch C, Gombert M, Minoo H. Classical modelization of symmetry effects in the dense high-temperature electron gas. Phys Lett A. 1978;66:381.
- Rogers FJ. Analytic electron-ion effective potentials for z ≤ 55. Phys Rev A. 1981;23:1008.
- Gombert MM, Minoo H, Deutsch C. Coulomb-like effective interactions for electrons with parallel spins at high temperature. Phys Rev A. 1984;29:940.
- Perrot F, Dharma-wardana MWC. Spin-polarized electron liquid at arbitrary temperatures:exchange-correlation energies, electron-distribution functions, and the static response functions. Phys Rev B. 2000;62:16536.
- Minoo H, Gombert M, Deutsch C. Temperature-dependent coulomb interactions in hydrogenic systems. Phys Rev A. 1981;23:924.
- Jerri A. Introduction to integral equations with applications. New York, NY: Wiley; 1999.
- Kress R. Linear integral equations. Berlin: Springer; 1999.
- Wazwaz AM. Linear and nonlinear integral equations, methods and applications. Beijing: Higher Education Press and Springer; 2011.
- Kashkar BH, Abbas SZ. Solution of initial value problem of bratu –type equation using modifications of homotopy perturbation method. Int J Comput Appl. 2017;162(5):44–49.
- Bratu G. Sur les équations intégrales non linèaires. Bull De La S M F. 1914;42:113–142.
- Karkowski J. Numerical experiments with the bratu equation in one, two and three dimensions. Comput Appl Math. 2013;32:231–244.
- Hichar S, Guerfi A, Douis S, et al. Application of nonlinear bratu’s equation in two and three dimensions to electrostatics. Reports Math Phys. 2015;76:283–290.
- Deleves L, Walsh J. Numerical solution of integral equations. Oxford: Clarendon Press; 1974.
- Al-Mezel SAR, Al-Solamy FRM, Ansari QH. Fixed point theory, variational analysis, and optimization. 13:978-1-4822-2207-4. 6000. Broken Sound Parkway NW Boca Raton: CRC Press; 2014.
- Ansorge R, Meis T, Tornig W. Iterative solution of nonlinear systems of equation. Germany: Proceedings of a Meeting held at Oberwolfach; 1982.
- Verlet L. Computer ”experiments” on classical fluids. i. thermodynamical properties of lennard-jones molecules. Phys Rev. 1967;159:98–103.
- Ladyzhenskaya OA. The method of finite differences. Vol. 49 of applied mathematical sciences. New York, NY: Springer Science and Business Media; 1985.
- Graziani FR, Batista VS, Benedict LX, et al. Large-scale molecular dynamics simulations of dense plasmas: the cimarron project. High Energy Density Phys. 2012;8:105–131.
- Alder BJ, Wainwright TE. Studies in molecular dynamics. i. general method. J Chem Phys. 1959;31:459-466.
- Frenkel D, Smit B. Understanding molecular simulation: from algorithms to applications. 2nd ed. San Diego: Academic Press; 2001.
- Huffman JD. Numerical methods for engineers and scientists. New York, NY: Marcel Dekker, INC; 2001.
- Allen MP, Tildesley DJ. Computer simulation of liquids. Oxford: University Press; 1989.