This article is cited in 1 paper

Applied mathematics

Estimates in the Taylor series method for polynomial total systems of PDEs

L. K. Babadzanjanz, I. Yu. Pototskaya, Yu. Yu. Pupysheva

St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: 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, total polynomial PDE system, polynomial system, numerical PDE system integration.

UDC: 519.63

MSC: 35F20, 65D30

Received: November 3, 2020
Accepted: January 15, 2021

Language: English

DOI: 10.21638/11701/spbu10.2021.103