Temat: Schrödinger equation - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Controllabilty and stability analysis on a group associated with Black-Scholes equation
Autorzy:: Tiwari, Archana
Bhattacharyya, Debanjana
Pati, K. C.
Powiązania:: https://bibliotekanauki.pl/articles/229513.pdf
Data publikacji:: 2020
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: Black-Scholes equation
Schrödinger equation
Lie group
optimal control
stability
numerical integration
Opis:: In this paper we have studied the driftless control system on a Lie group which arises due to the invariance of Black-Scholes equation by conformal transformations. These type of studies are possible as Black-Scholes equation can be mapped to one dimensional free Schrödinger equation. In particular we have studied the controllability, optimal control of the resulting dynamics as well as stability aspects of this system. We have also found out the trajectories of the states of the system through two unconventional integrators along with conventional Runge-Kutta integrator.
Źródło:: Archives of Control Sciences; 2020, 30, 3; 553-573
1230-2384
Pojawia się w:: Archives of Control Sciences
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Theoretical analysis on experiments in transformation of deep-water-waves
Autorzy:: Wilde, P.
Powiązania:: https://bibliotekanauki.pl/articles/241349.pdf
Data publikacji:: 2005
Wydawca:: Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:: water wave
stability
transformation
wave groups
non-linear Schrödinger differential equation
Opis:: The aim of the paper is to discuss the usefulness of the non-linear Schrödinger differential equation in the study of transformations of progressive deep water waves. Its solution compared with a regular Stokes type wave is essentially restricted to the first order approximation of the second one. The difference is that the Schrödinger equation introduces the concepts of a carrier wave and complex amplitude. In this way the dispersion relation of the third order Stokes expansion is taken into account. The analysis starts with regular, non breaking Stokes waves with large amplitudes as measured in our laboratory. The third order approximation is considered and compared with the corresponding solution of the Schrödinger equation. Then small periodic modifications are introduced in the time series fed into the control system of the generator. The approximation by trigonometric series is applied and the simplified analysis of superposition of very small modifications is used (higher powers of modifications are neglected). The Schrödinger non-linear equation is used in this analysis. The comparison of experimental and calculated envelopes is good, but for the surface elevations in space it is not as good. The approximation by trigonometric series is also applied to study the case of larger modifications. Finally the solutions of the Schrödinger equation corresponding to perfect solitons, are compared with the experimental data for cases where the measured surface elevations look almost like periodic solitons. This gives a reasonable approximation of the real behaviour in a very short space interval. It is not easy to get a good numerical description for the wave problem discussed as the waves are physically unstable. The results of the presented research will be used to establish an effective numerical procedure, stress the approximations introduced by the application of the Schrödinger differential equation and show how the theoretical solutions should be compared with the measured data.
Źródło:: Archives of Hydro-Engineering and Environmental Mechanics; 2005, 52, 3; 213-242
1231-3726
Pojawia się w:: Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:: Biblioteka Nauki

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