Constructive theory of scalar characteristic equations of the theory of radiation transport: II. algorithms for finding solutions and their analytic representations

Rogovtsov N. N.

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Constructive theory of scalar characteristic equations of the theory of radiation transport: II. algorithms for finding solutions and their analytic representations

机译：辐射传输理论的标量特征方程的构造理论：II。查找解决方案的算法及其解析表示

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We present methods for finding discrete spectra and derive analytic expressions for the eigenfunctions of scalar characteristic equations of the theory of radiation transport. We obtain new two-term recursion formulas and analytic representations for solutions of infinite tridiagonal systems of linear algebraic equations. We obtain analytic forms of the resolvents of scalar characteristic equations for phase functions square integrable on the closed interval [-1, 1]. In addition, we derive a general analytic expression for the Green function of a two-dimensional (with respect to the angular variables) integro-differential equation of the radiation transport for the case in which the phase functions satisfy the Holder condition on the closed interval [-1, 1].

机译：我们提出了寻找离散光谱的方法，并推导了辐射输运理论的标量特征方程特征函数的解析表达式。我们获得了线性代数方程的无限三对角线系统解的新的二元递推公式和解析表示。我们获得了在闭合区间[-1，1]上平方可积的相位函数的标量特征方程的解析形式。此外，对于在封闭区间上相位函数满足Holder条件的情况，我们导出了辐射传输的二维（关于角度变量）积分微分方程的格林函数的一般解析表达式[-1，1]。

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《Differential equations: A translation of differensial'nye uraveniya》 |2015年第5期|共13页
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Rogovtsov N. N.;
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正文语种 eng
中图分类微分方程、积分方程;
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1. Constructive theory of scalar characteristic equations of the theory of radiation transport: II. algorithms for finding solutions and their analytic representations [J] . Rogovtsov N. N. Differential equations: A translation of differensial'nye uraveniya . 2015,第5期

机译：辐射传输理论的标量特征方程的构造理论：II。查找解决方案的算法及其解析表示
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Constructive theory of scalar characteristic equations of the theory of radiation transport: II. algorithms for finding solutions and their analytic representations

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