Geodesic
An approximation algorithm for quadratic dynamic systems based on N. Chomsky's grammar for Taylor's formula
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 21-25

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Single-step methods for the approximate solution of the Cauchy problem for dynamic systems are discussed. It is shown that a numerical integration algorithm with a high degree of accuracy based on Taylor's formula can be proposed in the case of quadratic systems. An explicit estimate is given for the remainder term. The algorithm is based on N. Chomsky's generative grammar for the language of terms of Taylor's formula.
Keywords: dynamic system, quadratic system of equations, Cauchy problem, numerical solution, Taylor's formula, remainder term, error estimate, algorithm, context-free grammar. 
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A. A. Azamov; M. A. Bekimov. An approximation algorithm for quadratic dynamic systems based on N. Chomsky's grammar for Taylor's formula. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 21-25. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a1/