Abstract
This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demonstrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time (MECT) and optimal step-size (OS). In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.
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Wang, P., Huang, G. & Wang, Z. Analysis and application of multiple-precision computation and round-off error for nonlinear dynamical systems. Adv. Atmos. Sci. 23, 758–766 (2006). https://doi.org/10.1007/s00376-006-0758-y
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DOI: https://doi.org/10.1007/s00376-006-0758-y