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Fractional radiative transfer equation within Chebyshev spectral approach. (English) Zbl 1189.35359
Summary: We report the convergence of the Chebyshev polynomials combined with the SN method for the steady state transport equation using the fractional derivative. The procedure is based on the expansion of the angular flux in a truncated series of orthogonal polynomials that results in the transformation of the multidimensional problem into a system of fractional differential equations. The convergence of this approach is studied in the context of the multidimensional discrete-ordinates equations.
MSC:
35R11Fractional partial differential equations
26A33Fractional derivatives and integrals (real functions)
76R50Diffusion (fluid mechanics)
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