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一类半线性抛物型方程全离散Chebyshev拟谱逼近的大时间性态 被引量：1

THE LARGE TIME BEHAVIOR OF FULLY DISCRETE CHEBYSHEV PSEUDOSPECTRAL APPROXIMATE FOR A CLASS SEMILINEAR PARABOLIC EQUATIONS
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摘要 In thc paper, the nonperidic initial value problem for a class of semilinear parabolic equations is considered. We construct the full discrete Chebyshev pseu- dospectral scheme and analyze the error of approximate solution for it. We obtain the error estimation on large time using the local continuation method and the existence of approximate global attractor. This method can be applied to other nonlinear problems too. In thc paper, the nonperidic initial value problem for a class of semilinear parabolic equations is considered. We construct the full discrete Chebyshev pseu- dospectral scheme and analyze the error of approximate solution for it. We obtain the error estimation on large time using the local continuation method and the existence of approximate global attractor. This method can be applied to other nonlinear problems too.
作者 向新民 王鼎
机构地区 上海师范大学 上海市教育考试院
出处 《计算数学》 CSCD 北大核心 2002年第1期53-66,共14页 Mathematica Numerica Sinica
基金 国家自然科学基金(19871056) 上海市科技发展基金及上海高校科技发展基金资助项目.
关键词 半线性抛物型方程 Chebyshev拟谱逼近 大时间误差估计 近似吸引子 大时间性状 Semilinear parabolic equation, Chebyshev pseudospec- tral approximate, Error estimation on large time, Ap- proximate attractor
分类号 O241.5 [理学—计算数学]
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参考文献8

  • 1[1]D. Hoff, Stability convergence of finite difference methods for systems of non-linear reactiondiffusion equations, SIAM J. Numer. Anal., 15 (1978), 1161-1177.
  • 2[2]S. Larsson, The long-time behavior of finite element approximations of solutions to semilinear parabolic problems, SIAM J. Numer. Anal., 26 (1989), 348-365.
  • 3[3]J. M. Senz-serna & A. M. Stuart, A note on uniform in time error estimates for approximations to reaction-diffusion equations, SIMA J. Numer. Anal., 12 (1992), 457-462.
  • 4[4]C. Canuto & A. Qurteroni, Spectral and pseudospectral methods for parabolic problems with non-periodic boundary conditions, Calcalo, 18 (1981), 197-218.
  • 5[5]A.F.Timan, Approximate theory of real variable functions, Moscow, 1960.
  • 6[6]J.E.Pasciak, Spectral and pserdospectral mehtods for advection equations, Math. Compu.,35: 152 (1980), 1081-1092.
  • 7[7]R.Temam, Infinite dimensional dynamical system in mechanics and physics, Springer-Verlag, 1988.
  • 8[8]Shen J, Efficient spectral-Galerkin method II, Direct solvers of second and fourth equations by Chebyshev polynomials, SIAM J. Sci. Comput., 16 (1995), 74-87.

同被引文献3

  • 1Dan Henry. Geometric theory of semilinear parabolic equations[M]. New York: Springer-Verl ag, 1981 : 15-16.
  • 2Timan A F. Approximate theory of real variable functions[M]. Moscow: [s.n], 1960.
  • 3Pasciak J E. Spectral and pserdospectral methods for advection equations[J]. Math. Compu., 1980, 35 ( 152 ): 1 081-1 092.

引证文献1

计算数学
2002年 第1期

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