Wyniki wyszukiwania - BazTech

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Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations

Appadu Appanah Rao, Kelil Abey Sherif

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

377--409

EN

The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of the solution series in most cases and to overcome the deficiency that is mainly caused by unsatisfied conditions in other analytical techniques. We compare the approximate and numerical results with the exact solution for the two numerical experiments. The third numerical experiment does not have an exact solution and we compare profiles from the two methods vs the space domain at some values of time. This study provides us with information about which of the two methods are effective based on the numerical experiment chosen. Knowledge acquired will enable us to construct methods for other related partial differential equations such as stochastic Korteweg-de Vries (KdV), KdV-Burgers, and fractional KdV equations.

2

Investigation of a Jeffery-Hamel flow between two rectangular inclined smooth walls using the differential Transform Method

Patel N. D., Meher R.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 4

47--57

EN

In this article, the Differential Transform Method (DTM) is applied to derive a semi-analytic solution for the non-linear MHD (Magneto Hydro Dynamics) Jeffery-Hamel flow between rectangular inclined smooth planes. A non-linear ordinary differential equation of order four is obtained from Navier-Stokes equations using similar transformation. A comparison between DTM, PM (Perturbation Method) and numerical solution is shown here to validate the obtained results with its convergence analysis for different values of m and a Reynolds number in divergent channels.

3

Analityczne przybliżone rozwiązanie równania nieliniowego różniczkowego drugiego rzędu w dziedzinie zespolonej

Iwanow S., Orlov V.

Studia i Materiały / Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie

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2014

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Nr 2(8)

113--122

PL

Artykuł zawiera udowodnione twierdzenie na istnienie rozwiązania różniczkowego równania nieliniowego drugiego rzędu, którego prawa część jest wielomianem czwartego stopnia. W obszarze analityczności znaleziona została struktura jego rozwiązania przybliżonego. Dowód twierdzenia zawiera metodę zwaną majoranta. Taka metoda dotyczy całego badanego równania różniczkowego, a nie jego prawej części w przypadku klasycznym. Uzyskane wyniki zostały potwierdzone przez obliczenia.

EN

The theorem of solving the second-order nonlinear differential equation with polynomial part of the forth degree is proved and the structure of analytical approximate solution in analyticity region is presented in the article. When proving the theorem the majorant method is applied not to the right side of differential equation, but to the whole solution of differential equation. The results are provided with calculations.

4

A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

Cherniha R., Stachowska-Piętka J., Waniewski J.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

837--851

EN

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a three-component nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations as well as hydrostatic pressure. The model is developed in one spatial dimension approximation, and a governing equation for each of the variables is derived from physical principles. Under some assumptions the model can be simplified to obtain exact formulae for spatially non-uniform steady-state solutions. As a result, the exact formulae for fluid fluxes from blood to the tissue and across the tissue are constructed, together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.

5

Model matematyczny układu napędowego z silnikiem synchronicznym jako nauczyciel sztucznej sieci neuronowej

Chaban A, Lis M.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 12

320-323

PL

W pracy wykorzystując model matematyczny elektrycznego układu napędowego z silnikiem synchronicznym o biegunach jawnych, zaproponowano sztuczną siec neuronową do wyznaczenia momentu obciążenia. Model matematyczny układu zastosowano jako nauczyciela sieci neuronowej. Dla formułowania różniczkowych równań stanu wykorzystano metody wariacyjne. Wyniki symulacji komputerowych przedstawiono w postaci graficznej.

EN

In the paper the application of an artificial natural network is proposed in order to determine the load torque of electric motor. The mathematical model of electric drive system, based on a synchronous motor with salient poles, was used as a supervisor for the artificial neural network. The variational methods were used in order to formulate the differential state equations. Results of computer simulations are presented as graphs.