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A collocation‐type method for radiative transfer problems in a slab medium
Author(s) -
Razzaghi Mohsen,
Oppenheimer Seth,
Ahmad Falih
Publication year - 2001
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/1098-2760(20010305)28:5<307::aid-mop1026>3.0.co;2-2
Subject(s) - radiative transfer , collocation (remote sensing) , mathematics , interpolation (computer graphics) , mathematical analysis , algebraic equation , legendre polynomials , integral equation , collocation method , polynomial , slab , numerical analysis , differential equation , physics , nonlinear system , computer science , classical mechanics , optics , ordinary differential equation , motion (physics) , quantum mechanics , machine learning , geophysics
A numerical method for solving the radiative transfer equation in a slab medium with isotropic scattering is presented. The method is based upon constructing the m th‐degree interpolation polynomial to approximate the required solution using Legendre–Gauss–Lobatto collocation points. The differential and integral expressions which arise in the radiative transfer equation are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method, and a comparison is made with existing results. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 307–311, 2001.