Výsledky vyhledávání - "linear multistep methods"

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Long-term behaviour of symmetric partitioned linear multistep methods I. Global error and conservation of invariants

Autor: Cano, B., Durán, A., Rodríguez, M.

In this paper an asymptotic expansion of the global error on the stepsize for partitioned linear multistep methods is proved. This provides a tool to analyse the behaviour of these integrators with respect to error growth with time and conservation o

Externí odkaz: http://arxiv.org/abs/2411.13487

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Modified Patankar Linear Multistep methods for production-destruction systems

Autor: Izzo, Giuseppe, Messina, Eleonora, Pezzella, Mario, Vecchio, Antonia

Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discr

Externí odkaz: http://arxiv.org/abs/2407.12540

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A novel interpretation of Nesterov's acceleration via variable step-size linear multistep methods

Autor: Nozawa, Ryota, Sato, Shun, Matsuo, Takayasu

Nesterov's acceleration in continuous optimization can be understood in a novel way when Nesterov's accelerated gradient (NAG) method is considered as a linear multistep (LM) method for gradient flow. Although the NAG method for strongly convex funct

Externí odkaz: http://arxiv.org/abs/2404.10238

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Linear multistep methods with repeated global Richardson

Autor: Fekete, Imre, Lóczi, Lajos

In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for numerically solving initial-value problems of

Externí odkaz: http://arxiv.org/abs/2307.01345

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Error analysis based on inverse modified differential equations for discovery of dynamics using linear multistep methods and deep learning

Autor: Zhu, Aiqing, Wu, Sidi, Tang, Yifa

Along with the practical success of the discovery of dynamics using deep learning, the theoretical analysis of this approach has attracted increasing attention. Prior works have established the grid error estimation with auxiliary conditions for the

Externí odkaz: http://arxiv.org/abs/2209.12123

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