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PreprintCC BY-SA 4.0HAL

CONTINUOUS VERSUS DISCRETE STRUCTURES -DISCRETE EMBEDDING FORMALISMS AND CONTINUALIZATION METHODS

  • Jacky Cresson
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Abstract

We discuss the general problem of constructing discrete analogue of differential equations and the reverse one of constructing continuous limit of discrete systems. The first problem is solved using the point of view of discrete embeddings which is based ona a disccrete differential and integral calculus. As an application, we discuss the derivation of symplectic numerical scheme for Euler-Lagrange equations called variational integrators. by defining a discrete calculus of variations. The second problem is discussed via continualization methods.

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Cite

BibTeXRIS
BibTeX
@misc{cresson2026continuous,
  title = {{CONTINUOUS VERSUS DISCRETE STRUCTURES -DISCRETE EMBEDDING FORMALISMS AND CONTINUALIZATION METHODS}},
  author = {Jacky Cresson},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05742988v1},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - CONTINUOUS VERSUS DISCRETE STRUCTURES -DISCRETE EMBEDDING FORMALISMS AND CONTINUALIZATION METHODS
AU  - Jacky Cresson
PY  - 2026
DA  - 2026/09/08
PB  - HAL
UR  - https://hal.science/hal-05742988v1
AB  - We discuss the general problem of constructing discrete analogue of differential equations and the reverse one of constructing continuous limit of discrete systems. The first problem is solved using the point of view of discrete embeddings which is based ona a disccrete differential and integral calculus. As an application, we discuss the derivation of symplectic numerical scheme for Euler-Lagrange equations called variational integrators. by defining a discrete calculus of variations. The second problem is discussed via continualization methods.
ER  -