Solution of Systems of Ordinary and Partial Differential Equations by Quasi-Diagonal Matrices

Abstract

Methods of solving some rather complicated systems of ordinary and partial differential equations are described, including cases when some of them have eigenvalues or are non-linear. The equations are expressed in finite-difference form as “quasi-diagonal” matrix equations, and subroutines for solving these on the Ferranti Pegasus computer are described, including cases involving latent roots. The examples given are from the theory of gas discharges, but the method used are of much wider utility.