Padé approximant in radiative transfer

Wakil, S. A. El; Haggag, M. H.; Machali, H. M.; Saad, E. A.

doi:10.1016/0022-4073(84)90081-5

Cited by 11 publications

(3 citation statements)

References 9 publications

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“…Some approximate, numerical and rigorous solution for RTE for slab medium with anisotropic scattering have been reported. Examples of such solutions are: iterative (Sutton and Ozisik 1979), twoflux (Tien and Tong 1980), spherical harmonic (Domoto andWang 1974, Sutton andOzisik 1979), series expansion (Kumar et al 1990, Grcia andSiewer 1982), variational (Razi Nagri 1993), integral equation (Pomraning 1989, Razi Nagri 1993, eigenfunction expansion (Domke 1983), Pade approximation (El Wakil et al 1984), Generalized Eddington approximation (Wilson and Sen 1986) and linear spline approximation (Yi et al 1996).…”

Section: ∂I(y X)mentioning

confidence: 98%

On the applications of orthogonal functions in pattern recognition

Razzaghi

2005

SPIE Proceedings

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The properties of the hybrid functions which consists of block-pulse functions plus Chebyshev polynomials are presented. By using these hybrid functions, the differential and integral expressions which arise in the radiative transfer equation are converted into some linear systems of differential equations which can be solved for the unknown coefficient. A numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. Introduction.In the applications of remote sensing at optical wavelengths to different surfaces from satellite borne and high-resolution instruments, an understanding of the various physical mechanisms that contribute to the measured data is important. Accordingly, the solution of radiative transfer equation (RTE) has been utilized in

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Section: ∂I(y X)mentioning

confidence: 98%

On the applications of orthogonal functions in pattern recognition

Razzaghi

2005

SPIE Proceedings

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“…where c i are the expansion coefficients with c 0 = 1. The RTE in slab medium with anisotropic scattering has some numerical and rigorous solutions such as: two-flux [4,5], spherical harmonic [6,7], series expansion [8,9,10], integral equation [11,12], Padé approximation [13], iterative [6], variational [11,14,15], eigenfunction expansion [16,17], the linear spline approximation [1], the generalized Eddington approximation [3] and Spectral methods approximation [18,19,20].…”

Section: Radiative Transfer Equationsmentioning

confidence: 99%

The meshless method for solving radiative transfer problems in a slab medium based on radial basis functions

Rad,

Kazem,

Parand

2014

Preprint

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In this paper a numerical meshless method for solving the radiative transfer equations in a slab medium with an isotropic scattering is considered. The method is based on radial basis functions to approximate the solution of an integral-partial differential equation by using collocation method. For this purpose different applications of RBFs are used. To this end the numerical solutions are obtained without any mesh generation into the domain of the problems. The results of numerical experiments are compared with the existing results in illustrative examples to confirm the accuracy and efficiency of the presented scheme. Also the norm of the residual functions are obtained to show the convergence of the method.

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“…Some approximate, numerical and rigorous solutions of the RTE for a slab medium with anisotropic scattering have been reported. For example iterative [5], two-£ux [6,7], spherical harmonic [5,8], sries expansion [9^11], variational [12^14], integral equation [14,15], eigenfunction expansion [16,17], Pade approximation [18], generalized Eddington approximation [2] and linear spline approximation [1].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Radiative Transfer Problems in a Slab Medium by Galerkin-type Approximation Techniques

Razzaghi¹,

Oppenheimer²,

Ahmad³

2001

Phys. Scr.

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An approximate method for solving the radiative transfer equation in a slab medium with an isotropic scattering is proposed. The method is based upon constructing the double Legendre series to approximate the required solution using a Galerkin-type method. 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.

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Padé approximant in radiative transfer

Cited by 11 publications

References 9 publications

On the applications of orthogonal functions in pattern recognition

On the applications of orthogonal functions in pattern recognition

The meshless method for solving radiative transfer problems in a slab medium based on radial basis functions

Numerical Solution of Radiative Transfer Problems in a Slab Medium by Galerkin-type Approximation Techniques

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