Discrete Eigenvalues of the Radiative Transfer Equation with Legendre and Chebyshev Polynomials Solutions

Year 2023, Volume: 13 Issue: 4, 2594 - 2603, 01.12.2023

Hatice Asel Zilayaz , Halide Koklu

https://doi.org/10.21597/jist.1280514

Abstract

The radiation transfer equation has been considered for finite slab with isotropic scattering in homogeneous medium. The Legendre and Chebyshev polynomials are used to solve the radiative transfer equation to determine the discrete eigenvalues of the system for various single scattering albedo. The numerical results are performed for high level iterations of the PN and TN methods. The numerical values are tabulated and compared with the previous works. It is shown that our results are in very good agreement with previous studies.

Keywords

Eigenvalue Problem, Radiative Transfer, Chebyshev Polynomials

Legendre ve Chebyshev Polinomları Çözümü ile Radyasyon Transfer Denkleminin Kesikli Özdeğerleri

Abstract

Işınım transfer denklemi, homojen ortamda izotropik saçılmalı, sonlu plaka sistemi için ele alınmıştır. Legendre ve Chebyshev polinomları, çeşitli tekil saçılma albedolarıyla sistemin kesikli özdeğerlerini belirlemek üzere ışınım transfer denklemini çözmekte kullanılmıştır. Sayısal sonuçlar, PN ve TN yöntemlerinin yüksek seviye tekrarlama basamakları için gerçekleştirilmiştir. Sayısal değerler tablolaştırılmış ve önceki çalışmalarla karşılaştırılmıştır. Sonuçlarımızın önceki çalışmalarla çok iyi uyum içinde olduğu gösterilmiştir.

Keywords

Özdeğer Problemi, Işınım Transfer Denklemi, Chebyshev Polinomları

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