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An ordinary differential equation (ODE) can be split into simpler sub equations and each  of the  sub equations is  solved subsequently by a numerical method. Such a procedure  involves splitting error and numerical error caused by the time stepping methods applied to sub equations.  The aim of the paper is to present  an integral formula for the global error expansion of a splitting  procedure combined with any  numerical  ODE solver.

an international journal of optimization and control: theories and applications/e-an international journal of optimization and control: theories and applications

An integral formulation for the global error of Lie Trotter splitting scheme