A solution of the stationary transport equation in plane geometry

Meccanica ◽  
1983 ◽  
Vol 18 (2) ◽  
pp. 71-76
Author(s):  
Laura Bassi ◽  
Annalisa De Vito
Keyword(s):  
Transport Equation ◽  
Plane Geometry ◽  
Stationary Transport Equation

Approximate solutions to the half-space integral transport equation near a plane boundary

1980 ◽  
Vol 58 (9) ◽  
pp. 1291-1310 ◽  
Author(s):  
Michael S. Milgram
Keyword(s):  
Transport Equation ◽  
Half Space ◽  
Matrix Multiplication ◽  
Solution Space ◽  
Plane Geometry ◽  
Plane Boundary ◽  
Infinite Plane ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Integral Transport

A set of functions spanning the solution space of the integral transport equation near a boundary in semi-infinite plane geometry is obtained and used to reduce the problem to that of a system of linear algebraic equations. Expressions for the boundary angular flux are obtained by matrix multiplication, and the theory is extended to adjacent half-space problems by matching the angular flux at the boundary. Thus a unified theory is obtained for well-behaved arbitrary sources in semi-infinite plane geometry. Numerical results are given for both Milne's problem and the problem of constant production in adjacent half-spaces, and albedo problems in semi-infinite geometry. The solutions for the flux density are best near the boundary, and for the angular flux are best for angles near the plane of the boundary; it is conjectured that the theory will prove most useful when extended to arrays of finite slabs.

Fractional One-Dimensional Transport Equation Within Spectral Method Combined With Modified Adomian Decomposition Method

2009 ◽  
Author(s):  
Dumitru Baleanu ◽  
Abdelouahab Kadem
Keyword(s):  
Transport Equation ◽  
Spectral Method ◽  
Chebyshev Polynomials ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Plane Geometry ◽  
One Dimensional ◽  
Dimensional Plane ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper the Chebyshev polynomials technique combined with the modified Adomian decomposition method were applied to solve analytically the fractional transport equation in one-dimensional plane geometry.

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