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  1. 10 Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
  2. 10 Scientific Research of the Institute of Mathematics and Computer Science
  3. 6 International Journal of Applied Mechanics and Engineering
  4. 3 Archives of Hydro-Engineering and Environmental Mechanics
  5. 2 Applied Mechanics and Engineering
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  1. 5 Majchrzak E.
  2. 4 Ciesielski M.
  3. 3 Błaszczyk T.
  4. 3 Doležel I.
  5. 2 Czajkowski A. A.
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  1. 1 2023
  2. 2 2022
  3. 1 2020
  4. 3 2019
  5. 5 2018
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1
Content available A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation
Parajdi Lorand Gabriel, Precup Radu, Haplea Ioan Ştefan
International Journal of Applied Mathematics and Computer Science
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2023
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Vol. 33, no. 3
409--418
EN
A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka-Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.
2
Content available On the numerical solution of one inverse problem for a linearized two-dimensional system of Navier-Stokes equations
Jenaliyev Muvasharkhan, Ramazanov Murat, Yergaliyev Madi
Opuscula Mathematica
|
2022
|
Vol. 42, no. 5
709--725
EN
The paper studies the numerical solution of the inverse problem for a linearized two-dimensional system of Navier-Stokes equations in a circular cylinder with a final overdetermination condition. For a biharmonic operator in a circle, a generalized spectral problem has been posed. For the latter, a system of eigenfunctions and eigenvalues is constructed, which is used in the work for the numerical solution of the inverse problem in a circular cylinder with specific numerical data. Graphs illustrating the results of calculations are presented.
3
Content available remote Mathematical analysis of mass and heat transfer through arterial stenosis
Hussain Azad, Sarwar Luba, Akbar Sobia, Malik M. Y.
Journal of Power Technologies
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2022
|
Vol. 102, nr 3
88--95
EN
The article investigates the steady state flow of an incompressible fluid which is treated as a Williamson fluid through a stenoised region in the shape of cosine constriction. Blood is taken as a Williamson fluid. Mathematical formulation leads us to nonlinear compatibility and energy equations, which are then deciphered by the shooting technique to obtain the numerical solution. Suitable resemblance transformations are used to change partial differential equations into an embellished form of ordinary differential equations. Further, the consequences of the different parameters involved are shown by graphs and a conclusion is presented. Velocity and temperature fields are canvassed graphically for the distinct values of emerging parameters and discussed in tabular form. Skin friction and the coefficient of heat transfer are also covered in the discussion. The resulting Nusselt number curve exhibits negative deflection for variational values of λ and height of the stenosis δ.
4
Content available Analysis of co-flow jet effects on airfoil at moderate Reynolds numbers
Khoshnevis Amir, Yazdani Shima, Saimipour Erfan
Journal of Theoretical and Applied Mechanics
|
2020
|
Vol. 58 nr 3
685--695
EN
This paper investigates the performance of controlling Co-Flow Jet (CFJ) on NACA 0025 airfoil at five different Reynolds numbers of 5 · 104, 7.5 · 104, 105, 1.5 · 105, and 3 · 105. To conduct the numerical solution of the fluid flow, 2D incompressible and unsteady Reynolds- -averaged Navier-Stokes equations are solved using the SST-k-ω turbulence model. At all investigated Reynolds numbers, the lift coefficient enhances as the momentum coefficient increases, and its best performance is obtained at an angle of attack of (AoA) 15◦. It is also observed that using the CFJ is of greater importance at Re ≤ 105 than in other investigated cases.
5
Content available remote Numerical solution of a Casson nanofluid flow and heat transfer analysis between concentric cylinders
Hussain Azad, Javed Fousia, Nadeem Sohail
Journal of Power Technologies
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2019
|
Vol. 99, nr 1
25--30
EN
The current investigation deals with heat transfer of a non-newtonian fluid between two concentric cylinders. To describe the behavior of non-Newtonian fluid casson fluid model is used because of its various useful applications. The governing partial differential equations suchlike continuity, momentum, energy, solute concentration and nano-particle fraction equations are transubstantiated into non-linear ordinary differential equations with the assistance of resemblance alteration. Then those are numerically solved by the very efficient shooting method. Additionally, influences of distinct involved parameters are interpreted graphically. It is adhered that the velocity field shows inclined behavior due to the increment in the values of the casson parameter, so long as enhancing the temperature.
6
Content available The impact of radiation effect on MHD stagnation-point flow of a nanofluid over an exponentially stretching sheet in the presence of chemical reaction
Narender G., Sarma G. S., Govardhan K.
International Journal of Applied Mechanics and Engineering
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2019
|
Vol. 24, no. 4
125--139
EN
The present study is to investigate the effect of the chemical reaction parameter on stagnation point flow of magnetohydrodynamics field past an exponentially stretching sheet by considering a nanofluid. The problem is governed by governing coupled nonlinear partial differential equations with appropriate boundary conditions. The transformed non-dimensional and coupled governing ordinary differential equations are solved numerically using the fourth order Adams-Bashforth Moulton method. The effects of various dimensionless parameters on velocity, temperature and concentration fields are studied and then the results are presented in both tabular and graphical forms.
7
Content available remote A new approach for solving Bratu’s problem
Ghomanjani Fateme, Shateyi Stanford
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
336--346
EN
A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique. In this sequel, the obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets. The results display that this technique is accurate.
8
Content available Numerical solution through mathematical modelling of unsteady MHD flow past a semi-infinite vertical moving plate with chemical reaction and radiation
Bhandari A.
Studia Geotechnica et Mechanica
|
2018
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Vol. 40, nr 4
270--281
EN
In the present manuscript, unsteady magnetohydrodynamic (MHD) flow over a moving porous semi-infinite vertical plate with time-dependent suction has been studied in the presence of chemical reaction and radiation parameters. Time-dependent partial differential equations in the dimensionless form are solved numerically through mathematical modelling in COMSOL Multiphysics. The results are obtained for velocity, temperature and concentration profiles at different times. Steady state results are also presented for different values of physical parameters. The parameters involved in the problem are useful to change the characteristics of velocity, heat transfer and concentration profiles. The numerical solution of partial differential equations involved in the problem is obtained without sacrificing the relevant physical phenomena.
9
Content available Analytical and numerical solving of linear non-homogeneous differential equations of the first-order with changeable coefficients by using constant variation method and application of Mathematica program
Czajkowski A. A., Oleszak W. K., Dyrdał J.
Problemy Nauk Stosowanych
|
2018
|
T. 8
5--20
EN
Introduction and aim: The paper presents the analytical and numerical algorithm of solving linear nonhomogeneous equations of the first order with changeable coefficients. The aim of the work is to show the algorithms for solving equations both analytically and numerically. The additional aim is to show numerical algorithms and graphical interpretation of solutions. Material and methods: Some selected equations have been chosen from the subject literature. In the solutions the constant variation method has been presented. Results: The paper presents the selected linear non-homogeneous equations of the first order with changeable coefficients containing exponential, logarithmic, trigonometric and cyclometric functions. Conclusion: Taking into account the constant variation method it is possible to solve the first order linear nonhomogeneous differential equations with changeable coefficients. Using the Mathematica program it is possible quickly get a solution and create its graphical interpretation.
PL
Wstęp i cel: W pracy pokazano algorytmy analityczny i numeryczny rozwiązywania równań różniczkowych liniowych niejednorodnych pierwszego rzędu o zmiennych współczynnikach. Celem pracy jest pokazanie algorytmu rozwiązywania równań zarówno sposobem analitycznym jak i numerycznym. Ponadto również dodatkowym celem jest pokazanie algorytmów numerycznych oraz interpretacji graficznej rozwiązań. Materiał i metody: Wybrane równania zaczerpnięto z literatury przedmiotu. W rozwiązaniach równań zastosowano metodę wariacji stałej. Wyniki: W pracy opracowano wybrane równania różniczkowe liniowe niejednorodne pierwszego rzędu o zmiennych współczynnikach zawierających funkcje wykładnicze, logarytmiczne, trygonometryczne i arcus. Wniosek: Stosując metodę uzmienniania stałej jest możliwe rozwiązywanie równań różniczkowych liniowych niejednorodnych pierwszego rzędu o zmiennych współczynnikach. Wykorzystując program Mathematica można szybko uzyskać rozwiązanie oraz sporządzić jego interpretację graficzną.
10
Content available Analytical and numerical solving of linear non-homogeneous differential equations of the second-order with changeable coefficients by using constant variation method and application of Mathematica program
Czajkowski A. A., Oleszak W. K., Skorny G. P., Udała R.
Problemy Nauk Stosowanych
|
2018
|
T. 8
21--38
EN
Introduction and aim: The paper presents the analytical and numerical algorithm of solving linear nonhomogeneous equations of the second order with changeable coefficients. The aim of the work is to show the algorithms for solving equations both analytically and numerically. The additional aim is to make some graphical interpretation of solutions. Material and methods: Some selected equations have been chosen from the subject literature. In the solutions the constant variation method has been presented. Results: The paper presents the selected linear non-homogeneous equations of the second order with constant coefficients containing linear, homographic, logarithmic and trigonometric functions. Conclusion: Taking into account the constant variation method it is possible to solve the second order linear non-homogeneous differential equations with changeable coefficients. Using the Mathematica program it is possible quickly get a solution and create its graphical interpretation.
PL
Wstęp i cel: W pracy pokazano algorytm analityczny i numeryczny rozwiązywania równań różniczkowych liniowych niejednorodnych drugiego rzędu o zmiennych współczynnikach. Celem pracy jest pokazanie algorytmu rozwiązywania równań zarówno sposobem analitycznym jak i numerycznym. Ponadto dodatkowym celem jest interpretacji graficznej rozwiązań. Materiał i metody: Wybrane równania zaczerpnięto z literatury przedmiotu. W rozwiażanich równań zastosowano metodę wariacji stałej. Wyniki: W pracy opracowano wybrane równania różniczkowe liniowe niejednorodne drugiego rzędu o zmiennych współczynnikach zawierających funkcje liniowe, homograficzne, logarytmiczne i trygonometryczne. Wniosek: Stosując metodę uzmienniania stałej jest możliwe rozwiązywanie równań różniczkowych liniowych niejednorodnych drugiego rzędu o zmiennych współczynnikach. Wykorzystując program Mathematica można szybko uzyskać rozwiązanie oraz sporządzić jego interpretację graficzną.
11
Content available Investigation of the Stability and Convergence of Difference Schemes for the Three-dimensional Equations of the Atmospheric Boundary Layer
Temirbekov A. N., Urmashev B. A., Gromaszek K.
International Journal of Electronics and Telecommunications
|
2018
|
Vol. 64, No. 3
391--396
EN
In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved.
12
Content available Engineering example of the constraint forces in non-holonomic mechanical: forklift-truck robot motion. Part I
Haddout S., Guennoun M. A., Chen Z.
Archives of Control Sciences
|
2018
|
Vol. 28, No. 3
483--506
EN
In the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a Forklift-truck robot motion. This method of the geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. On the other hand, the equations of motion of a Forklift-truck robot are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem. The results of numerical solutions of constrained equations of motion, derived within the theory, are presented.
13
Content available Probabilistic and Statistical Modelling of the Harmful Transport Impurities in the Atmosphere from Motor Vehicles
Wojcik W., Adikanova S., Malgazhdarov Y. A., Madiyarov M. N., Myrzagaliyeva A. B., Temirbekov N. M., Junisbekov M., Pawłowski L.
Rocznik Ochrona Środowiska
|
2017
|
Tom 19
795--808
EN
The aim of the work is to create a mathematical model for the distribution of emissions from vehicles. In this article, it was proposed to use the probabilistic and statistical approach for modelling the distribution of harmful impurities in the atmosphere from vehicles using the example of the Ust-Kamenogorsk city. Using a simplified methodology of stochastic modelling, it is possible to construct effective numerical computational algorithms that significantly reduce the amount of computation without losing their accuracy.
PL
Celem pracy jest stworzenie matematycznego modelu rozprzestrzeniania się zanieczyszczeń z pojazdów. W tym artykule zaproponowano zastosowanie podejścia probabilistycznego i statystycznego do modelowania rozprzestrzeniania się szkodliwych zanieczyszczeń w atmosferze z pojazdów na przykładzie miasta Ust-Kamenogorsk. Stosując uproszczoną metodologię modelowania stochastycznego, można konstruować skuteczne numeryczne algorytmy obliczeniowe, które znacznie redukują ilość obliczeń bez utraty dokładności.
14
Content available The verification of the estimation of transport and sorption parameters in the MATLAB environment. A column test
Okońska M., Kaczmarek M., Małoszewski P., Marciniak M.
Geology, Geophysics and Environment
|
2017
|
Vol. 43, no. 3
213--227
EN
Mathematical modelling of the migration of pollutants in the groundwater environment requires knowledge of the values of transport and sorption parameters. The aim of this study was 1) to determine the values of advection, dispersion and sorption parameters of selected tracers that are transported through a porous medium, and 2) to verify the applied parameters estimation procedure. The authors examined the migration of a solution containing conservative and reactive tracers (chloride, nitrate, lithium and ammonium ions) through a sample of medium sand. The soil sample for the column test was taken from an aquifer near the Tursko groundwater intake (Wielkopolska province, Poland). The parameter estimation procedure, conducted in the MATLAB environment, included the numerical solution of the differential equations of transport and sorption, and the application of the numerical optimization method. During the identification, the authors tested twelve mathematical models including the advection-dispersion model, as well as single and hybrid (i.e. two-site) sorption models. The authors made a comparison of parameter values obtained by means of the global and local optimization method. The fitting quality was assessed by calculating the root mean square error RMSE and correlation coefficient r. As a result of the research, the authors determined the values of the advection-dispersion parameters: hydraulic conductivity k, effective porosity n e, and longitudinal dispersivity α. The authors found out that the nature oflithium ions migration is best captured by the single sorption model (equilibrium sorption), whereas the nature of ammonium ions migration is by the hybrid model with irreversible sorption. Lithium ions on the tested soil revealed low sorption intensity, ammonium ions showed medium intensity, while nitrate ions were transported at the same rate as chloride ions, exhibiting no retardation. The verification of parameter estimation in the MATLAB environment was carried out by comparing it against the alternative, well-known and often tested method, based on analytical solutions of the transport and sorption equation, combined with optimization within the FIELD and KLUTE-STEP programmes.
15
Content available remote Stability estimates for Discrete duality finite volume scheme of Heston model
Handlovicova A.
Computer Methods in Materials Science
|
2017
|
Vol. 17, No. 2
101--110
EN
Tensor diffusion equation represents an important model in many fields of science. We focused our attention to the problem which arises in financial mathematics and is known as 2D Heston model. Stability estimates for discrete duality finite volume scheme for proposed model is presented. Numerical experiments using proposed method and comparing it with previous numerical scheme are included.
PL
Tensorowe równanie dyfuzji jest ważnym modelem w wielu obszarach nauki. W pracy skupiono się na problemie, który występuje w matematyce finansowej i jest znany jako dwuwymiarowy model Hestona. Zaprezentowano oszacowanie stabilności dla dyskretnego, dualnego schematu objętości skończonych. W pracy zamieszczono wyniki numerycznych eksperymentów przeprowadzonych z wykorzystaniem zaproponowani metody, które porównano z opublikowanymi wcześniej schematami numerycznymi.
16
Content available remote Properties of numerical solution of the deformation and stability problem in shallow conical shells under external pressure
Krasovsky V., Karasev A.
Roads and Bridges - Drogi i Mosty
|
2016
|
Vol. 15, no. 2
117--135
EN
The paper presents an analysis of a numerical solution in the ANSYS software to three problems related to determination of deformations and stability of closed shallow conical shells under external pressure: 1) linear (bifurcation) problem of determining the critical pressure; 2) geometrically non-linear problem of shell deformation and buckling to determine the limit pressure using axisymmetric finite elements (FE); 3) solution to the same problem as set out in 2, yet using 4-node shell elements. The solutions presented in the paper concern the stationary state of a simply supported and fixed shell. Shallow conical shells are applied as load bearing and protective elements of bridge structures.
PL
W pracy wykonano analizę rozwiązania numerycznego w środowisku oprogramowania ANSYS trzech zadań wyznaczenia deformacji i stateczności zamkniętych małowyniosłych powłok stożkowych, poddanych działaniu ciśnienia zewnętrznego: 1) zadania liniowego (bifurkacyjnego) określenia wartości krytycznej ciśnienia; 2) geometrycznie nieliniowego zadania deformacji i wyboczenia powłoki oraz wyznaczenia ciśnienia granicznego przy wykorzystaniu osiowo-symetrycznych elementów skończonych (ES); 3) rozwiązania zadania 2, lecz przy wykorzystaniu czterowęzłowych elementów powłokowych. Przedstawiono rozwiązania stanu stacjonarnego powłoki swobodnie podpartej i utwierdzonej. Małowyniosłe powłoki stożkowe wykorzystywane są jako elementy nośne i ochronne konstrukcji mostowych.
17
Content available Model of magnetic gun with respecting eddy currents
Leubner K., Doležel I., Laga R.
Poznan University of Technology Academic Journals. Electrical Engineering
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2015
|
No. 81
21--29
EN
A sophisticated mathematical model of the magnetic gun is presented and solved numerically. The model consists of three strongly non-linear and non-stationary differential equations describing the time-dependent distribution of magnetic field in the device, current in the field circuit and movement of the projectile. The numerical solution is carried out in the application Agros2D based on a fully adaptive higher-order finite element method. The results are processed in Wolfram Mathematica. The methodology is illustrated by an example and selected results are compared with experiment.
18
Content available Numerical solution of non-homogenous fractional oscillator equation in integral form
Ciesielski M., Błaszczyk T.
Journal of Theoretical and Applied Mechanics
|
2015
|
Vol. 53 nr 4
959--968
EN
In this paper, a non-homogenous fractional oscillator equation in finite time interval is considered. The fractional equation with derivatives of order α ∈ (0, 1] is transformed into its corresponding integral form. Next, a numerical solution of the integral form of the considered equation is presented. In the final part of this paper, some examples of numerical solutions of the considered equation are shown.
19
Content available Application of the multi-step differential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells
Zurigat M., Ababneh M.
Journal of Mathematics and Applications
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2015
|
Vol. 38
171--180
EN
Human T-cell Lymphotropic Virus I (HTLV-I) infection of CD4+ T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transform method is implemented to give approximate solutions of fractional modle of HTLV-I infection of CD4+ T-cells. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method in the case of intger-order derivatives. The suggested method is efficient as the Runge-Kutta method. Some plots are presented to show the reliability and simplicity of the method.
20
Content available Numerical Simulations for Solving Fuzzy Fractional Differential Equations by max-min Improved Euler Methods
Khan N. A., Razzaq O. A., Riaz F.
Journal of Applied Computer Science Methods
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2015
|
Vol. 7 No. 1
53--83
EN
In this paper, an extension is introduced into Max-Min Improved Euler methods for solving initial value problems of fuzzy fractional differential equations (FFDEs). Two modified fractional Euler type methods have been proposed and investigated to obtain numerical solutions of linear and nonlinear FFDEs. The proposed algorithms are tested on various illustrative examples. Exact values are also simulated to compare and discuss the closeness and accuracy of approximations so obtained. Comparatively, tables and graphs results reveal the complete reliability, efficiency and accuracy of the proposed methods.
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