Abstract
The paper presents a new recursive method using Taylor series to solve the states of time invariant as well as time varying control systems. In traditional approach, the Taylor series had been used by well known operational matrix for integration, whereas this proposition does not follow the same method. This approach is recursive in nature and thereby avoids the complexity of using operational matrix of fixed dimension. Additionally, computational burden and memory requirement is greatly reduced. If equal number of recursion points are considered, the second order Taylor series solution is always more efficient than the first order Taylor series solution. But, the first order Taylor series can approach the accuracy of the second order Taylor series solution at the cost of more recursion points, i.e., increasing the computational burden. This has been studied numerically. Three examples are treated and the results obtained are compared with the exact solutions via related tables and graphs. The present approach is attractive because of its straightforward approach.
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Ghosh, S. (2019). Analysis of Linear Time Invariant and Time Varying Dynamic Systems via Taylor Series Using a New Recursive Algorithm. In: Chattopadhyay, S., Roy, T., Sengupta, S., Berger-Vachon, C. (eds) Modelling and Simulation in Science, Technology and Engineering Mathematics. MS-17 2017. Advances in Intelligent Systems and Computing, vol 749. Springer, Cham. https://doi.org/10.1007/978-3-319-74808-5_34
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DOI: https://doi.org/10.1007/978-3-319-74808-5_34
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