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Lithuanian Mathematical Journal

, Volume 36, Issue 1, pp 8–16 | Cite as

On convergence and stability of difference schemes for derivative nonlinear evolution equations

  • F. Ivanauskas
  • T. Meškauskas
Article

Abstract

We investigate the initial-boundary value problem for the nonlinear equation system
$$\frac{{\partial u}}{{\partial t}} = A\frac{{\partial ^2 u}}{{\partial x^2 }} + f(u) + g(u)\frac{{\partial u}}{{\partial x}},$$
whereA is a complex diagonal matrix,f andg are complex vector-functions. The convergence and stability in theW 2 2 norm of the proposed Crank-Nicolson type difference schemes is proved. No restrictions on the ratio of time and space grid steps are assumed.

Keywords

Iterative Method Difference Scheme Sobolev Norm Nonlinear SchrOdinger Equation Difference Problem 
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.

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • F. Ivanauskas
  • T. Meškauskas

There are no affiliations available

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