A Study of the Dynamic Difference Approximations on Time Scales
نویسندگان
چکیده
Various dynamic equations have been used extensively in modeling many important natural phenomena, such as the population or epidemic growth with unpredictable jump sizes, motion control of impulsive robot movements, and prediction of irregular option markets. Since dynamic derivatives are basic building blocks of most dynamic equations, it has been crucial to approximate the derivatives to yield computable discrete equations for numerical solutions. This motivates our investigations. This paper proposes a class of feasible approximation methods for the first and second order noncrossed dynamic derivatives. Applicable local error estimates are derived and discussed. Numerical experiments are given to illustrate our results. AMS Subject Classifications: 34A45, 39A13, 74H15, 74S20.
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