Global Error Control in a Lotka-Volterra system using the RKQ Algorithm

Abstract

We use explicit, implicit and symplectic versions of Euler's method to solve a Lotka-Volterra system. We implement local error control via local extrapolation, and we use the RKQ algorithm, which provides global error control. We find that local extrapolation, although providing acceptable control of local error, does not control global error. However, RKQ achieves both local and global error control in a stepwise manner. A symplectic form of Euler's method preserves the first integral of the system if the stepsize is fixed, but not if an explicit method is used in the local extrapolation mode. However, the explicit form of RKQ does preserve the first integral, because it is able to control global error.