on the solution of nonlinear matrix integral equations in transport theory
Bowden, Robert L.
Zweifel, P. F.
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The coupled nonlinear matrix integral equations for the matrices X (z) and Y (z) which factor the dispersion matrix Λ (z) of multigroup transport theory are studied in a Banach space X. By utilizing fixed‐point theorems we are able to show that iterative solutions converge uniquely to the ’’physical solution’’ in a certain sphere of X. Both isotropic and anisotropic scattering are considered.