Iterative solution of large linear systems and heavy particle collisions

In this paper the solution of large sparse linear systems of algebraic equations arising from the discretization of coupled Boltzmann partial integro-differential equations, which model ion-ion recombination processes in dense gases, is discussed. The advantages and limitations of various representations of these equations is provided. A detailed analysis is given of the derivation and structure of the coefficient matrix A of the resultant algebraic equations. The need for preconditioning the algebraic equations through the calculation of the condition number of the matrix A is highlighted. Approximate methods of computing thermolecular recombination rate coefficients via the Debye-Smoluchowski equation and diffusion models in energy space are also briefly discussed