On the solution of nonlinear rate equations by matrix inversion

Abstract

In this paper an idea of T. Carleman is used to imbed a finite set of nonlinear rate equations into an infinite set of linear equations. The matrix operator associated with the linear equations is generally a triangular matrix whose matrix elements are matrices. Since an explicit expression is available for the inverse of such a matrix, an algorithm can be found to yield the solution of the original set of nonlinear equations.