In this work it is reviewed the variational approach for some Transport Problems. Let X be a convex domain in Rn, and V a compact set. For that, it is considered the following equation:
ψt(x,v,t)+v·ψ(x,v,t)+h(x,μ)ψ(x,v,t)==Vk(x,v,v)ψ(x,v,t)dv+q(x,v,t)(1)
where x represents the spatial variable in a domain D, v an element of a compact set V, Ψ is the angular flux, h(x,v) the collision frequency, k(x,v,v’) the scattering kernel function and q(x,v) the source function. It is put the attention in the construction of the quadratic functional J which appears in variational approaches for transport theory (for example, the Vladimirov functional). Some properties of this functional in a proper functional framework, in order to determine the minimum for J are considered. First, the general formulation is studied. Then an algorithm is given for minimizing the functional J for two remarkable problems: spherical harmonic method and spectral collocation method. A program associated to this algorithm is worked in a computer algebraic system, and also was depeloped a version in a high level language.
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