Advertisement

Lithuanian Mathematical Journal

, Volume 33, Issue 1, pp 12–22 | Cite as

On the difference scheme for a nonlinear diffusion-reaction-type problem

  • R. Čiegis
  • M. Meilūnas
Article

Keywords

Difference Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Mascagni, The backward Euler method for numerical solution of the Hodkin-Huxley equation of nerve conduction,SIAM J. Numer. Analys.,27, 941–962 (1990).Google Scholar
  2. 2.
    R. Čiegis, On the convergence inC norm of symmetric difference schemes for nonlinear evolution problems,Lith. Math. J.,32, 147–161 (1992).Google Scholar
  3. 3.
    Raim. Čiegis and Rem. Čiegis, Mathematical modeling of laser heating of metal. Spatial problem,Lith. Math. J.,31, 491–496 (1991).Google Scholar
  4. 4.
    B. N. Klochkov, A. M. Reinman, and J. A. Stepaniantz, A nonstationary flow of the fluid in the tubes of an active viscoelastic material,Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 94–102 (1985).Google Scholar
  5. 5.
    N. N. Abrashin, Difference schemes for hyperbolic nonlinear equations. II,Differents. Uravn.,11, 294–308 (1975).Google Scholar
  6. 6.
    A. D. Liashko and E. M. Fedotov, The investigation of nonlinear two-step operator-difference schemes with weights,Differents. Uravn.,21, 1217–1227 (1985).Google Scholar
  7. 7.
    L. F. Jukhno, On the nature of the net method convergence in the solution of nonlinear evolutionary problems,Dokl. Akad. Nauk SSSR,228, 325–328 (1976).Google Scholar
  8. 8.
    N. G. Zhadaeva, On the convergence of the difference method for the solution of nonlinear evolution problems,Differents. Uravn.,16, 1710–1713 (1980).Google Scholar
  9. 9.
    P. P. Matus and L. V. Stanishevskaya, On the unconditional convergence of difference schemes for nonstationary, nonlinear problems of mathematical physics,Differents. Uravn.,27, 1203–1219 (1991).Google Scholar
  10. 10.
    Raim. Čiegis and Rem. Čiegis,On the stability of economical difference schemes for problems with nonlinear connected boundary condition, in: Mathematical Modelling and Applied Mathematics, Proceedings of the IMACS International Conference on Mathematical Modelling and Applied Mathematics, Moscow, USSR, 18–23 June 1990, North-Holland, Amsterdam (1992), pp. 89–97.Google Scholar
  11. 11.
    A. A. Samarskii,The Theory of Difference Schemes [in Russian], Nauka, Moscow (1983).Google Scholar
  12. 12.
    C. Johnson, Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations,SIAM J. Numer. Anal.,25, 908–926 (1988).Google Scholar
  13. 13.
    G. I. Marchouk and V. V. Shaydourov,Increase of Accuracy of Difference Schemes [in Russian], Nauka, Moscow (1979).Google Scholar
  14. 14.
    R. Kanapėnas, S. Norvaišas, R. Petruškevičius, and R. Čiegis,Numerical solution of the problem describing laser metal heating, in: Differential Equations and Their Applications [in Russian], No. 43, IMI, Vilnius (1988), pp. 49–67.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • R. Čiegis
    • 1
  • M. Meilūnas
    • 2
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania
  2. 2.Vilnius University Computer CenterVilniusLithuania

Personalised recommendations