Abstract
The electron distribution function plays a key role in the quantitative study of various properties of electrons moving through a gas and is characterized as a solution of the Boltzmann transport equation. Simplication of this model results in a non-self-adjoint second-order elliptic partial differential equation with variable coefficients. The complexity of the coefficients precludes the use of a coordinate transformation to remove second-order cross-derivative terms, and the nonmodelness of the boundary value problem necessitates rather novel applications of various tools of numerical analysis for successful solution. Due to the non-self-adjointness, any consistent finite difference model is bound to be nonsymmetric; however, a finite difference scheme is devised which is “almost symmetric.” Iterative solution of the resulting difference equations is analyzed and an acceleration strategy for convergence is devised. Numerical results are included for a typical problem involving in excess of 5000 Mesh points. This problem was solved on the UNIVAC 1106 in less than 6 min of CPU time.
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