Geodesic
Estimates in the Taylor series method for polynomial total systems of PDEs
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 1, pp. 27-39

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Many of total systems of PDEs can be reduced to the polynomial form. As was shown by various authors, one of the best methods for the numerical solution of the initial value problem for ODE systems is the Taylor Series Method (TSM). In the article, the authors consider the Cauchy problem for the total polynomial PDE system, obtain the recurrence formulas for Taylor coefficients, and then formulate and prove a theorem on the accuracy of its solutions by TSM.
Keywords: Taylor Series Method, polynomial system, numerical PDE system integration.
Mots-clés : total polynomial PDE system 
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     title = {Estimates in the {Taylor} series method for polynomial total systems of {PDEs}},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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L. K. Babadzanjanz; I. Yu. Pototskaya; Yu. Yu. Pupysheva. Estimates in the Taylor series method for polynomial total systems of PDEs. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 1, pp. 27-39. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a2/