Weighted iterative solutions of linear differential equations and heat conduction of ideal gases in moment theory (Q854661)

The authors consider a system of nonhomogeneous linear differential equations, with no boundary conditions, which is replaced by a fixed point problem with a differential operator \(G\) which is normally required to be ``contractive'' and ``non-expansive''. As the differential operators are generally not contractive and non-expansive, the authors propose an iterative approximation with gradually decreasing weight depending on the iteration. Conditions for convergence are established and applied to a problem of one- dimensional stationary heat conduction of ideal gases between two coaxial cylinderical walls.