Quadratized Taylor series methods for ODE numerical integration

Borri, Alessandro; Carravetta, Francesco; Palumbo, Pasquale

doi:10.1016/j.amc.2023.128237

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2024

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Cited by 2 publications

References 21 publications

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Koopman-Hill Stability Computation of Periodic Orbits in Polynomial Dynamical Systems Using a Real-Valued Quadratic Harmonic Balance Formulation

Bayer,

Leine,

Thomas

et al. 2024

Preprint

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Koopman-Hill Stability Computation of Periodic Orbits in Polynomial Dynamical Systems Using a Real-Valued Quadratic Harmonic Balance Formulation

Bayer,

Leine,

Thomas

et al. 2024

Preprint

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Taylor's formula on the separating complex plane and its applications

Li,

Fan,

Sun

2024

HSET

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This article begins by exploring split-complex numbers, also known as dual or double numbers, a mathematical concept that extends the real number system by creating a commutative ring with a zero divisor. Furthermore, the paper extends the Taylor series theory from the real analysis domain to the domain of split-complex numbers, thereby establishing the corresponding Taylor formula on the split-complex plane. The introduction of split-complex numbers opens up new perspectives and provides new tools for the modeling and analysis of quantum systems. In the field of electromagnetism, the application of split-complex numbers also demonstrates its potential, contributing to a more precise description of the behavior of electromagnetic fields under specific conditions. These theoretical advancements are expected to further promote research in the field of split-complex analysis, playing a more critical role in important branches of physics such as quantum mechanics and electromagnetism, thereby facilitating the development of related theories and the emergence of innovative practical applications.

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Quadratized Taylor series methods for ODE numerical integration

Cited by 2 publications

References 21 publications

Koopman-Hill Stability Computation of Periodic Orbits in Polynomial Dynamical Systems Using a Real-Valued Quadratic Harmonic Balance Formulation

Koopman-Hill Stability Computation of Periodic Orbits in Polynomial Dynamical Systems Using a Real-Valued Quadratic Harmonic Balance Formulation

Taylor's formula on the separating complex plane and its applications

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