再生核空间中求解定态对流扩散方程<sup>*</sup>

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再生核空间中求解定态对流扩散方程^*

基金项目: * 国家自然科学基金

摘要: 本文在再生核空间W₂¹中,给出定态对流扩散方程的一种级数形式的解析解,此解析解具有如下特点:1)解是由精确的形式给出;2)解是显式计算,不须解方程组;3)在数值求解中,每增加一个基数项,近似解的误差在空间范数意义下单调下降。最后对[2]中的算例,进行了计算,结果比[2]中给出的渐近解精度高。
- 再生核 /
- 对流扩散方程 /
- 解析解
Abstract: In this paper,in the space W₂¹ that possesses restoring nucleus,we obtain analytic solutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics:(1)they ave given in the accurate form:(2)they can be calculated in the explicit way,without solving the eguations;(3)the error of the approximate solution will be monotonically decreased under the meaning of the norm of the spaces when a cardinal term is added in the procedure of numerical solution.Finally,we calculated the example in [2] the result shows that our solution is more accurate than that in[2].
- restoring nuclesus /
- convection diffusion equation /
- analytic solutions

[1]	陆金甫、关治,定态对流扩散方程的修正Dsnnis格式,计算物理,3(2)(1986),234-240.
[2]	吴启光,修正Dsnnis格式的渐近解,数值计算与计算机应用,(2)(1991),90-94.
[3]	崔明根、邓中兴,W₂¹空间中的最佳插值逼近算子,计算数学,(2)(1988).
[4]	崔明根、邓中兴,W₂¹空间中的最佳Hermite算子,计算物理,(2)(1988).
[5]	崔明根等,第二类Fredholm积分方程解析解,数学进展,(3)(1988).
[6]	Zhang Mian.Cui Ming-gen and Deng Zhong-xing.A new uniformly convergent iterative method by interpolation.where error decreases monotonically.J.Computional.Mathematics.3.4(1985),365-372.