Error Analysis and the Role of Permutation in Dynamic Iteration Schemes

Zubik‐Kowal, Barbara

doi:10.1007/978-3-030-48186-5_12

Cited by 4 publications

(2 citation statements)

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“…We now rearrange the components in (12), append Equation (10), and obtain the following new system for z = z(t),…”

Section: Coefficient-informed Transformations For Dynamic Iterationsmentioning

confidence: 99%

“…The focus of the present paper is not on computational issues but on the framework of dynamic iterations in a broad sense, addressing the question of how to use the magnitudes of the given parameters to construct transformations that reduce the number of required dynamic iterations. It has been recently shown in Zubik‐Kowal [10] that using appropriate permutations of the equations in a given system offers a way to reduce the number of required dynamic iterations. In contrast to this approach, the transformations introduced in the present paper are not constructed through the use of permutations and are instead based on new complex parameters, which are related to the eigenvectors of the associated matrices.…”

Section: Introductionmentioning

confidence: 99%

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A physics‐informed order‐of‐magnitude approach to handling dynamic iterations applied to models of physical systems: Theoretical framework

Zubik‐Kowal

2023

Math Methods in App Sciences

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In this paper, we consider ‐dimensional systems of differential equations applied to model a range of physical phenomena, where represents any positive integer. The defining characteristic that we focus on are the magnitudes of the inherent physical parameters, which are frequently of different orders of magnitude for various physical systems. This property, inherent to the given physical problems, can be exploited to reduce the problems into a set of much simpler subproblems, expanding our ability to gain physical insight in terms of the underlying simpler subproblems. These orders of magnitude motivate the choice of a specific class of transformations that can be chosen to reduce the number of required dynamic iterations in a sequence‐based approach to examining such systems. This is also useful for the development of proof techniques for proving properties of mathematical models, such as their well‐posedness.

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“…We now rearrange the components in (12), append Equation (10), and obtain the following new system for z = z(t),…”

Section: Coefficient-informed Transformations For Dynamic Iterationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%