This paper considers the convergence of one-step ordinary differential equation (ode) methods for systems of partial differential equations which have been spatially discretized using finite differences. The analysis presented in the paper uses the ode notions of logarithmic matrix norm and C-stability to obtain convergence results for the discretized system of odes.

Two examples are presented to demonstrate the manner in which the results may be applied to specific problems. In general, the application of the results to problems of interest would be quite difficult. The results are also somewhat pessimistic for many problems of interest. Finally, they do not apply to many other problems of interest (e.g., hyperbolic systems). The paper is well written and should be of some interest to readers concerned with method-of-lines solution techniques.