Result Details
Effective solution of nonlinear DAEs problems using Taylor series method
Šátek Václav, Ing., Ph.D., DITS (FIT)
Nečasová Gabriela, Ing., Ph.D., DITS (FIT)
Most methods for solving ordinary differential equations use a limited order to calculate the results. The higher-order method based on the Taylor series presented in this article can use as many terms of the Taylor series as necessary to obtain a stable and accurate solution. When solving nonlinear problems using this method, the solution can be complex. This paper introduces a new approach to solving nonlinear problems using the explicit Taylor series method. It compares this new approach against the previously used approach and the state-of-the-art solvers in MATLAB software.
Taylor series method; MATLAB; initial value problems; nonlinear ordinary differential equations; differential-algebraic equations
@article{BUT197169,
author="Petr {Veigend} and Václav {Šátek} and Gabriela {Nečasová}",
title="Effective solution of nonlinear DAEs problems using Taylor series method",
journal="Demonstratio Mathematica",
year="2026",
volume="59",
number="1",
pages="19",
doi="10.1515/dema-2025-0216",
issn="0420-1213",
url="https://degruyterbrill.com/document/doi/10.1515/dema-2025-0216/html"
}