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


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.


Iterative Method Difference Scheme Sobolev Norm Nonlinear SchrOdinger Equation Difference Problem 
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© Plenum Publishing Corporation 1996

Authors and Affiliations

  • F. Ivanauskas
  • T. Meškauskas

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