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首页> 外文期刊>Journal of Computational Physics >SEVERAL SYMBOLIC AUGMENTED CHEBYSHEV EXPANSIONS FOR SOLVING EQUATION OF RADIATIVE TRANSFER
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SEVERAL SYMBOLIC AUGMENTED CHEBYSHEV EXPANSIONS FOR SOLVING EQUATION OF RADIATIVE TRANSFER

机译：几种符号增强的切比雪夫展开式用于求解辐射传递方程

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摘要

Three expansion methods are described using Chebyshev polynomials of the first kind for solving the integral form of the equation of radiative transfer in an isotropically scattering, absorbing, and emitting plane-parallel medium. With the aid of symbolic computation, the unknown expansion coefficients associated with this choice of basis functions are shown to permit analytic resolution. A unified and systematic solution treatment is offered using the projection methods of collocation, Ritz-Galerkin, and weighted-Galerkin. Numerical results a re presented contrasting the th ree expansion methods and comparing them with existing benchmark results. New theoretical results are presented illustrating rigorous error bounds, residual characteristics, accuracy, and convergence rates. (C) 1995 Academic Press, Inc. [References: 50]
机译：使用第一类Chebyshev多项式描述了三种扩展方法，用于求解各向同性散射，吸收和发射平面平行介质中辐射传递方程的积分形式。借助于符号计算，示出了与该基础函数的选择相关联的未知膨胀系数以允许解析分辨率。使用搭配，Ritz-Galerkin和weighted-Galerkin的投影方法提供了一个统一而系统的解决方案。给出了数值结果，对比了三种扩展方法，并将其与现有基准结果进行了比较。提出了新的理论结果，说明了严格的误差范围，残留特征，准确性和收敛速度。 （C）1995 Academic Press，Inc. [参考：50]

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