Polynomial approximation of nonlinear differential systems with prefixed accuracy |
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| Authors: | Benito Chen-Charpentier Lucas Jódar Aleksey S Telyakovskiy |
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| Institution: | 1. Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA;2. Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, 46022 Valencia, Spain;3. Department of Mathematics and Statistics, University of Nevada at Reno, Reno, NV 89557, USA;1. Faculty of Technology, De Montfort University, Leicester LE1 9BH, UK;2. Shell Centre, London SE1 7LZ, UK;3. University of Nigeria, Nsukka, Nigeria |
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| Abstract: | This paper presents a method for constructing polynomial approximations of the solutions of nonlinear initial value systems of differential equations. Given an a priori chosen accuracy, the degree of the vector polynomial can be adapted so that the approximate solution has the required precision. The method is based on the AI-method of Dzyadyk developed for the scalar case, and the computational cost is shown to be competitive with other methods. |
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