Abstract
This paper derives sufficient conditions for the absolute stability of a certain multi-rate method of numerical integration of systems of first-order ODE's which have been separated into two subsystems, the second system being made up of the faster-response equation. It is assumed that the subsystems are integrated with fourth-order and third-order Runge-Kutta methods, respectively. It is shown that there will be regions of stability, provided the original system is sufficiently diagonally dominant. If the subsystems are weakly coupled, the regions of stability are nearly as large as the classical regions.
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