Wyniki wyszukiwania - BazTech

1

Pontryagin’s maximum principle for optimal control problems governed by nonlinear impulsive differential equations

Leiva Hugo

Journal of Mathematics and Applications

|

2023

|

Vol. 46

15-68

EN

In this paper, we derive the Pontryagin’s maximum principle for optimal control problems governed by nonlinear impulsive differential equations. Our method is based on Dubovitskii-Milyutin theory, but in doing so, we assumed that the linear variational impulsive differential equation around the optimal solution is exactly controllable, which can be satisfied in many cases. Then, we consider an example as an application of the main result. After that, we study the case when the differential equation is of neutral type. Finally, several possible problems are proposed for future research where the differential equation, the constraints, the time scale, the impulses, etc. are changed.

2

Computational scheme for a differential difference equation with a large delay in convection term

Erla Srinivas, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

|

2023

|

Vol. 28, no. 2

34--48

EN

A computational scheme for the solution of layer behaviour differential equation involving a large delay in the derivative term is devised using numerical integration. If the delay is greater than the perturbation parameter, the layer structure of the solution is no longer preserved, and the solution oscillates. A numerical method is devised with the support of a specific kind of mesh in order to reduce the error and regulate the layered structure of the solution with a fitting parameter. The scheme is discussed for convergence. The maximum errors in the solution are tabulated and compared to other methods in the literature to verify the accuracy of the numerical method. Using this specific kind of mesh with and without the fitting parameter, we also studied the layer and oscillatory behavior of the solution with a large delay.

3

Difference scheme for differential-difference problems with small shifts arising in computational model of neuronal variability

Kodipaka Mamatha, Emineni Siva Prasad, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

|

2022

|

Vol. 27, no. 1

91--106

EN

The solution of differential-difference equations with small shifts having layer behaviour is the subject of this study. A difference scheme is proposed to solve this equation using a non-uniform grid. With the non-uniform grid, finite - difference estimates are derived for the first and second-order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the tridiagonal system algorithm. Convergence of the scheme is examined. Various numerical simulations are presented to demonstrate the validity of the scheme. In contrast to other techniques, maximum errors in the solution are organized to support the method. The layer behaviour in the solutions of the examples is depicted in graphs.

4

Computational approach to solving a layered behaviour differential equation with large delay using quadrature scheme

Pandi A., Mudavath Lalu, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

|

2022

|

Vol. 27, no. 4

117--137

EN

This paper deals with the computational approach to solving the singularly perturbed differential equation with a large delay in the differentiated term using the two-point Gaussian quadrature. If the delay is bigger than the perturbed parameter, the layer behaviour of the solution is destroyed, and the solution becomes oscillatory. With the help of a special type mesh, a numerical scheme consisting of a fitting parameter is developed to minimize the error and to control the layer structure in the solution. The scheme is studied for convergence. Compared with other methods in the literature, the maximum defects in the approach are tabularized to validate the competency of the numerical approach. In the suggested technique, we additionally focused on the effect of a large delay on the layer structure or oscillatory behaviour of the solutions using a special form of mesh with and without a fitting parameter. The effect of the fitting parameter is demonstrated in graphs to show its impact on the layer of the solution.

5

Entire and meromorphic solutions for systems of the differential difference equations

Xu Hong Yan, Li Hong, Ding Xin

Demonstratio Mathematica

|

2022

|

Vol. 55, nr 1

676--694

EN

With the help of the Nevanlinna theory of meromorphic functions, the purpose of this article is to describe the existence and the forms of transcendental entire and meromorphic solutions for several systems of the quadratic trinomial functional equations: {f(z)2+2αf(z)g(z+c)+g(z+c)2=1,g(z)2+2αg(z)f(z+c)+f(z+c)2=1, {f(z+c)2+2αf(z+c)g'(z)+g'(z)2=1,g(z+c)2+2αg(z+c)f'(z)+f'(z)2=1, and {f(z+c)2+2αf(z+c)g′′(z)+g′′(z)2=1,g(z+c)2+2αg(z+c)f′′(z)+f′′(z)2=1. We obtain a series of results on the forms of the entire solutions with finite order for such systems, which are some improvements and generalizations of the previous theorems given by Gao et al. Moreover, we provide some examples to explain the existence and forms of solutions for such systems in each case.

6

The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters

Winnicki Ireneusz, Jasinski Janusz, Pietrek Sławomir, Kroszczynski Krzysztof

Advances in Geodesy and Geoinformation

|

2022

|

Vol. 71, no. 2

art. no. e23, 2022

EN

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used third-order 3x3 pixels Laplace contour filters including the difference schemes used to derive them. The authors focused on the mathematical properties of the Laplace filters. The basic reasons of the differences of the properties were studied and indicated using their transfer functions and modified differential equations. The relations between the transfer function for the differential Laplace operator and its difference operators were described and presented graphically. The impact of the corner elements of the masks on the results was discussed. This is a theoretical work. The basic research conducted here refers to a few practical examples which are illustrations of the derived conclusions.We are aware that unambiguous and even categorical final statements as well as indication of areas of the results application always require numerous experiments and frequent dissemination of the results. Therefore, we present only a concise procedure of determination of the mathematical properties of the Laplace contour filters matrices. In the next paper we shall present the spectral characteristic of the fifth order filters of the Laplace type.

7

The mathematical characteristic of the fifth order Laplace contour filters used in digital image processing

Winnicki Ireneusz, Pietrek Sławomir, Jasinski Janusz, Kroszczynski Krzysztof

Advances in Geodesy and Geoinformation

|

2022

|

Vol. 71, no. 2

art. no. e26, 2022

EN

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used fifth-order pixels Laplace filters including the difference schemes used to derive them (finite difference method – FDM and finite element method – FEM). The results of the research concerning third-order pixels matrices of the convolution Laplace filters used for digital processing of images were presented in our previous paper: The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters is presented byWinnicki et al. (2022). As previously, the authors focused on the mathematical properties of the Laplace filters: their transfer functions and modified differential equations (MDE). The relations between the transfer function for the differential Laplace operator and its difference operators are described and presented here in graphical form. The impact of the corner elements of the masks on the results is also discussed. A transfer function, is a function characterizing properties of the difference schemes applied to approximate differential operators. Since they are relations derived in both types of spaces (continuous and discrete), comparing them facilitates the assessment of the applied approximation method.

8

On nonlinear fractional neutral differential equation with the ψ-Caputo fractional derivative

Nabil Tamer

Journal of Mathematics and Applications

|

2020

|

Vol. 43

99--112

EN

In this article, the solvability of fractional neutral differential equation involving ψ-Caputo fractional operator is considered usinga Krasnoselskii’s fixed point approach. Also, we establish the uniquenessof the solution under certain conditions. Ulam stabilities for the proposedproblem are discussed. Finally, examples are displayed to aid the applicability of the theory results.

9

Comparison of the approximate solution with the solution of the differential equation for the static problem of deep-profiled sandwich panels

Pozorska Jolanta

Journal of Applied Mathematics and Computational Mechanics

|

2020

|

Vol. 19, nr 4

81--88

EN

The article presents an approximate method of solving the problem of statics of sandwich elements with deep-profiled facings. This method is compared with the widely accepted theory of sandwich beams. The example of uniformly loaded, simply-supported, single-span sandwich beam is presented. The results of displacements, internal forces and stresses obtained by both methods are compared. The results confirm the good compliance of the presented solutions, in particular in terms of displacements.

10

A nonlocal problem for a differential operator of even order with involution

Kalenyuk Petro I., Baranetskij Yaroslav O., Kolyasa Lubov I.

Journal of Applied Analysis

|

2020

|

Vol. 26, nr 2

297--307

EN

We study a nonlocal problem for ordinary differential equations of 2n-order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.

11

The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

Usta Fuat, Sarıkaya Mehmet Zeki

Demonstratio Mathematica

|

2019

|

Vol. 52, nr 1

204--212

EN

In this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.

12

Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

Bandura Andriy, Skaskiv Oleh, Smolovyk Liana

Demonstratio Mathematica

|

2019

|

Vol. 52, nr 1

482--489

EN

In the paper we investigate slice holomorphic functions F : Cn→C having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 +tb : t∈C} for an arbitrary z0∈Cn and for the fixed direction b∈Cn \ {0}, and (∃m0∈Z+) (∀m∈Z+) (∀z∈Cn) the following inequality holds [wzór], where L : Cn→R+ is a positive continuous function, [wzór] for p≥2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differentia equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

13

Regular classes of linear extensions of dynamical systems on a torus

Morawiak M.

Silesian Journal of Pure and Applied Mathematics

|

2018

|

Vol. 8, iss. 1

21--31

EN

The paper presents new methods of construction of the Lyapunov function for some sets of linear extensions of dynamic systems on torus.The paper is divided into two parts. The first part contains a brief theoretical introduction. In the second part are presented results of study and examples.

14

On regularity of linear systems of differential equations

Morawiak M.

Silesian Journal of Pure and Applied Mathematics

|

2018

|

Vol. 8, iss. 1

5--20

EN

The paper presents the theorems about regularity of systems of differential equations. The paper is divided into two parts. The first part contains a theoretical introduction. The second part contains theorems which allows to determine the regularity of the system using the generalized Lyapunov function.

15

Mathematical model of bats’ subpopulations development

Dawidowicz A. L., Poskrobko A.

Mathematica Applicanda

|

2018

|

Vol. 46, no. 1

49--57

EN

The paper deals with the description of the mathematical model of bats’ subpopulations and fission-fusion societies development. The model is based on the system of ordinary differential equations. Bats’ behaviour and their searching strategy is presented on the basis of cavity roosting bats living in Białowieża Forest located in Poland. Theoretical results are illustrated by a computer simulation and its comparison with biological remarks.

PL

Artykuł dotyczy opisu matematycznego modelu subpopulacji nietoperzy oraz rozwoju procesu zasiedlania nowych dziupli. Model oparty jest na systemie równań różniczkowych zwyczajnych. Zachowania nietoperzy i ich strategie poszukiwań przedstawiono na podstawie obserwacji nietoperzy zamieszkujących dziuple w Puszczy Białowieskiej. Wyniki teoretyczne ilustruje symulacja komputerowa i jej porównanie z uwagami biologicznymi.

16

Fractional-order discrete model of an independent wheel electrical drive of the autonomous platform

Bąkała M., Nowakowski J., Ostalczyk P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2018

|

Vol. 66, nr 4

433--440

EN

In the paper the linear time-invariant fractional-order models of the separated wheel closed-loop electrical drive of the autonomous platform are considered. As a reference model one considers the classical model described by the second-order linear difference equation. Two discrete-time fractional-order models are considered: non-commensurate and commensurate. According to the sum of the squared error criterion (SSE) one compares two-parameter integer-order model with the four-parameter non-commensurate and three-parameter commensurate fractional-order ones. Three mathematical models are built and simulated. The computer simulation results are compared with measured velocity of the real autonomous platform separate wheel closed-loop electrical drive.

17

Solution approaches to differential equations of mechanical system dynamics: a case study of car suspension system

Terefe Tesfaye O., Lemu Hirpa G

Advances in Science and Technology. Research Journal

|

2018

|

Vol. 12, no 2

266--273

EN

Solution of a dynamic system is commonly demanding when analytical approaches are used. In order to solve numerically, describing the motion dynamics using differential equations is becoming indispensable. In this article, Newton’s second law of motion is used to derive the equation of motion the governing equation of the dynamic system. A quarter model of the suspension system of a car is used as a case and sinusoidal road profile input was considered for modeling. The state space representation was used to reduce the second order differential equation of the dynamic system of suspension model to the first order differential equation. Among the available numerical methods to solve differential equations, Euler method has been employed and the differential equation is coded MATLAB. The numerical result of the second degree of freedom, quarter suspension system demonstrated that the approach of using numerical solution to a differential equation of dynamic system is suitable to easily simulate and visualize the system performance.

18

Zastosowanie metody wielokrokowej Geara oraz metody niejawnej Rungego-Kutty do badania dynamiki obwodu zawierającego cewkę nieliniową

Kolańska-Płuska J., Kawala-Janik A.

Przegląd Elektrotechniczny

|

2017

|

R. 93, nr 4

23--25

PL

Praca dotyczy zastosowania metody wielokrokowej Geara oraz wybranych metod niejawnych IRK do rozwiązania układu równań różniczkowych zwyczajnych, opisujących obwód zawierający cewkę nieliniową. Zostanie przedstawiony model takiej cewki oraz jej opis za pomocą wybranych zmiennych stanu. Zostanie również przedstawiony program do badania dynamiki cewki opracowany w języku C#, w którym zaimplementowano metody niejawne RK: RADAU IIA, Gaussa-Legendre'a, Lobatto III C oraz metody wielokrokowe.

EN

The work concerns the application of the multistep Gear and selected IRK implicit methods to solve the system of ordinary differential equations describing a circuit containing non-linear coil. In this paper - model of the coil and its description with the use of selected state variables will also be presented. This paper will also show application for dynamics examination of the circuit written in C#, in which the following implicit RK methods were implemented: Radau IIA, Gauss-Legendre, Lobatto III C and the multistep method.

19

Eigen value approach to generalized thermoelastic interactions in an unbounded body with circular cylindrical cavity without energy dissipation

Chakraborty S.

International Journal of Applied Mechanics and Engineering

|

2017

|

Vol. 22, no. 4

811--825

EN

The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.

20

The controllability of nonlinear implicit fractional delay dynamical systems

Joice Nirmala R., Balachandran K.

International Journal of Applied Mathematics and Computer Science

|

2017

|

Vol. 27, no. 3

501--513

EN

This paper is concerned with the controllability of nonlinear fractional delay dynamical systems with implicit fractional derivatives for multiple delays and distributed delays in control variables. Sufficient conditions are obtained by using the Darbo fixed point theorem. Further, examples are given to illustrate the theory.