Rational Spectral Approximation Of The Klein-gordon-schrodinger Equation In Unbounded Domain A Matter Of Time

In recent years, infinite dimensional dynamical systems have made great development [12],[17],[18]. With the thorough research on these and computer ability increasing quickly, people are paying more and more attention to relational numerical study. The mostly discussion is how to numerical simulate, concering error estimate in long-time, the existence of approximate attractor, well-posedness of solution and numerical solution and dimension estimate and so on, now there are much study [5],[15]. spectral method is important numerical method, but it is very hard so that research is a less.Klein-Gordon-Schr(?)dinger(KGS) equtions presented itself in duplicate Schrodinger field and real Klein-Gordonfield initially [14]. It is very important in mathmetics and phisics. Many papers studied their periods problem and the problem on bounded field [6],[7],[9]. In this paper, we study KGS equations with weakly damp using Chebyshev rational spectral. We introduce some marks and lemmas before we construct Chebyshev rational spectral formation of semi-discrete with respect to space. Then we obtian the error estimate for the approximate solution and the existence of approximate attractor An, and besides, we prove the upper semi-continuty on the global attractor. Finally, we establish rational spectral formation of discrete with regard to time and space, and gained the error estimate in the finite-time in the abstract.