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Tytuł:
On the semi-analytic technique to deal with nonlinear fractional differential equations
Autorzy:
Khirsariya, Sagar R.
Rao, Snehal B.
Powiązania:
https://bibliotekanauki.pl/articles/2202059.pdf
Data publikacji:
2023
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional differential equation
logistic equation
Fornberg-Whitham equation
homotopy perturbation method
Sawi transform
ułamkowe równanie różniczkowe
równanie logistyczne
równanie Fornberga-Whithama
metoda perturbacji homotopii
Opis:
In this article, we present a novel hybrid approach, by combining the Sawi transform with the homotopy perturbation method, to achieve the approximate and analytic solutions of nonlinear fractional differential equations (ODE as well as PDE) using the time-fractional Caputo derivative. The proposed algorithm is faster and simple compared to other iterative methods. The Sawi transform is used along with the homotopy perturbation method to accelerate the convergence of the series solution. The results discussed using calculations, graphs and tables are compatible for comparison with other known methods like the residual power series method and the exact solution which are discussed in the literature.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 1; 17--30
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions of Benjamin-Bona-Mahony, modified Camassa-Holm and Degasperis Procesi equations using an iterative method
Autorzy:
Kumar, Manoj
Powiązania:
https://bibliotekanauki.pl/articles/2202030.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
nonlinear Bejamin-Bona-Mahony equation
modified Camassa-Holm equation
modified Degasperis-Procesi equation
Daftardar-Gejji and Jafari method
homotopy perturbation method
Adomian decomposition method
nieliniowe równanie Bejamina-Bony-Mahony'ego
zmodyfikowane równanie Camassy-Holma
zmodyfikowane równanie Degasperisa-Procesiego
metoda Daftardara-Gejji i Jafari
metoda perturbacji homotopii
metoda dekompozycji Adomiana
Opis:
In the present paper, we solve the non-linear Benjamin-Bona-Mahony, modified Camassa-Holm, and Degasperis-Procesi equations using an iterative method introduced by Daftardar-Gejji and Jafari. Results are compared with those obtained by other iterative methods such as the Adomian decomposition method and homotopy perturbation method. It is observed that the proposed method is computationally inexpensive and yields more accurate solutions than the Adomian decomposition method and the homotopy perturbation method.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 3; 59--72
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Homotopy Perturbation Method of Hydromagnetic Flow and Heat Transfer of a Casson Fluid over an Exponentially Shrinking Sheet
Autorzy:
Murugesan, Thiagarajan
Varshini, S.
Kumar, M. Dinesh
Powiązania:
https://bibliotekanauki.pl/articles/1031915.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Casson Fluid
Homotopy Perturbation method
MHD
Runge-Kutta method
suction
Opis:
Nonlinear hydromagnetic flow and heat transfer of a Casson fluid over an exponentially shrinking sheet has been investigated. The fluid is assumed to be viscous, incompressible and electrically conducting. The similarity transformations are applied to reduce the non-linear partial differential equations into the non-linear ordinary differential equations. Homotopy Perturbation Method is used to solve the resulting non-linear differential equations under appropriate boundary conditions. The impact of Casson fluid parameter, magnetic interaction parameter, suction parameter and Prandtl number on both velocity and temperature profiles are shown graphically. Thermal boundary layer thickness decreases with increasing Prandtl number. Effect of Casson fluid parameter is to reduce both the velocity and temperature. Quantities of physical interest such as skin-friction coefficient, non-dimensional rate of heat transfer are solved numerically. A comparison reveals a remarkable agreement between the Homotopy Perturbation Method and Runge-Kutta fourth order method.
Źródło:
World Scientific News; 2020, 140; 59-78
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A comparative study of differential transformation and homotopy perturbation methods for transient combustion analysis for iron micro-particles in a gaseous oxidizing medium
Autorzy:
Yinusa, A. A.
Sobamowo, M. G.
Powiązania:
https://bibliotekanauki.pl/articles/1046539.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Differential transformation method
Homotopy perturbation method
Iron particle combustion
Temperature distribution
Thermal radiation
Opis:
In this paper, a comparative study of differential transformation and homotopy perturbation methods for transient combustion analysis of iron micro-particles in a gaseous oxidizing medium is presented. Also, parametric studies are carried out to properly understand the reaction of the process and the associated burning time. Thermal radiation effect from the external surface of burning particle and variation of iron particle density with temperature are considered. The solutions obtained by DTM and HPM are compared with those of the fourth order Runge-Kutta numerical method. Results show that DTM has more accurate results between the two approximate analytical methods considered. Also, results show that by increasing the heat realized parameter, combustion temperature increased and it faster reaches to its constant value. It is envisaged that the present study will create tremendous insight into means of properly managing combustible micro particles exiting factories and production process organization.
Źródło:
World Scientific News; 2019, 138, 2; 93-112
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Study on the Effects of Inclined Magnetic Field, Flow Medium Porosity and Thermal Radiation on Free Convection of Casson Nanofluid over a Vertical Plate
Autorzy:
Sobamowo, M. G.
Yinusa, A. A.
Makinde, O. D.
Powiązania:
https://bibliotekanauki.pl/articles/1046549.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Casson nanofluid
Flow medium porosity
Free convection
Inclined magnetic field
Thermal radiation
Variational homotopy perturbation method
Opis:
In this paper, variational homotopy perturbation method with Padé approximant technique is applied to investigate the impacts of inclined magnetic field, flow medium porosity and thermal radiation on free convection flow and heat transfer of Casson nanofluids over a vertical plate. The accuracies of the developed analytical methods are verified by comparing the results of the analytical solutions with the results of past works as presented in literature. Thereafter, the analytical solutions are used to investigate the effects of thermal radiation; Prandtl number, nanoparticles volume-fraction, shape and type on the flow and heat transfer behaviour of various nanofluids over the flat plate. It is observed that both the velocity and temperature of the nanofluid as well viscous and thermal boundary layers increase with increase in the radiation parameter. The velocity and temperature of the nanofluid decreases and increases, respectively as the Prandtl number and volume-fraction of the nanoparticles in the basefluid increase. The maximum decrease in velocity and maximum increase in temperature are caused lamina shaped nanoparticle and followed by platelets, cylinder, bricks and sphere-shaped nanoparticles, respectively. It is hoped that the present study will enhance the understanding of free convection boundary-layer problems under the influence of thermal radiation as applied in various engineering processes.
Źródło:
World Scientific News; 2019, 138, 1; 1-64
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergences Analysis from the Solution Function of the Riccati Fractional Differential Equation by Using Modified Homotopy Perturbation Method
Autorzy:
Sevira, Nurazizah M.
Rusyaman, Endang
Firdaniza, Firdaniza
Subiyanto, Subiyanto
Supian, Sudradjat
Powiązania:
https://bibliotekanauki.pl/articles/1059423.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Convergent
Differential Equation
Fractional
Modified Homotopy Perturbation Method
Riccati
Opis:
A Fractional differential equation is an equation that contains derivatives with an order of fractional numbers. Same with natural number order differential equations, this type of equation is divided into linear and nonlinear fractional differential equations. One of the equations that include nonlinear fractional differential equation is Riccati fractional differential equation (RFDE). Various methods have been applied to find solutions for fractional differential equations Riccati, one of them is the Modified Homotopy Perturbation Method (MHPM) which is a modification of the Homotopy Perturbation Method by Zaid Odibat and Shaher Momani. In this study, the MHPM was used to find solutions for fractional differential equations Riccati, which were then used to analyze the convergence of the function sequences of the solution. The result shows us that the order sequence of Riccati fractional differential equation which converges to a number causes the solution function sequence of Riccati fractional differential equation will converge to the function of the solution of Riccati fractional differential equation with the order of this number.
Źródło:
World Scientific News; 2019, 128, 2; 71-87
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Heat transfer analysis of non-Newtonian natural convective fluid flow using Homotopy Perturbation and Daftardar-Gejiji & Jafari Methods
Autorzy:
Adeleye, Olurotimi
Yinusa, Ahmed
Powiązania:
https://bibliotekanauki.pl/articles/122431.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
non-Newtonian fluid
natural convection
vertically infinite plates
Daftardar-Gejiji & Jafari Method
DJM
Homotopy Perturbation Method
HPM
ciecz nieniutonowska
konwekcja naturalna
metoda Daftardar-Gejiji i Jafari
metoda perturbacji homotopii
Opis:
In this paper, the analytical solution of natural convective heat transfer of a non-Newtonian fluid flow between two vertical infinite plates using the Homotopy Perturbation Method (HPM) and Daftardar-Gejiji & Jafari Method (DJM) is presented. The heat transfer problem of natural convection is observed in many engineering fields including geothermal systems, heat exchangers, petroleum reservoirs, nuclear waste reserves, etc. The problem which is modelled as fully coupled nonlinear ordinary differential equations requires special analytical techniques for its solution. The solutions are obtained using an exact analytical method: the Homotopy Perturbation Method (HPM) and a semi-analytical method: the Daftardar-Gejiji & Jafari Method (DJM). These solutions are compared with solutions obtained from the Runge-Kutta numerical method. The results are in good agreement with the numerical solutions. The effects of the Eckert number, Prandtl number and the non-Newtonian fluid viscosity parameter on the non-dimensional temperature and velocity of the fluid are investigated. The results obtained from the analytical method show that the method can be applied to predict excellent results of the problem and can be used for parametric studies of the problem. From the results, it is shown that when the Prandtl number and the Eckert number are increased, there is an increase in both temperature and fluid flow velocity.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 5-18
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Effect of variable viscosity on MHD inclined arterial blood flow with chemical reaction
Autorzy:
Tripathi, B.
Sharma, B. K.
Powiązania:
https://bibliotekanauki.pl/articles/264659.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
magnetohydrodynamika
lepkość
reakcja chemiczna
magnetohydrodynamical fluid
homotopy perturbation method
variable viscosity
chemical reaction
Opis:
In this paper, we present the mathematical study of heat and mass transfer effects on an arterial blood flow under the influence of an applied magnetic field with chemical reaction. A case of mild stenosis is considered in a non-tapered artery which is inclined at an angle γ from the axis. The variable viscosity of the blood is considered varying with the hematocrit ratio. Governing non-linear differential equations have been solved by using an analytical scheme, homotopy perturbation method to obtain the solution for the velocity, temperature and concentration profiles of the blood flow. For having an adequate insight to blood flow behavior through a stenosed artery, graphs have been plotted for wall shear stress, velocity, temperature and concentration profiles with varying values of the applied magnetic field, chemical reaction parameter and porosity parameter. The results show that in an inclined artery, the magnitude of the wall shear stress at stenosis throat increases as values of the applied magnetic field increase while it reduces as the values of both the chemical reaction and porosity parameters increase. Contour plots have been plotted to show the variations of the velocity profile of blood flow as the values of the height of the stenosis as well as the influence of the applied magnetic field increase.
Źródło:
International Journal of Applied Mechanics and Engineering; 2018, 23, 3; 767-785
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The stability conditions of the cubic damping Van der Pol-Duffing oscillator using the HPM with the frequency-expansion technology
Autorzy:
El-Dib, Y. O.
Powiązania:
https://bibliotekanauki.pl/articles/122293.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
homotopy perturbation method
nonlinear oscillators
cubic nonlinear damping van der Pol’s equation
nonlinear frequency analysis
stability analysis
metoda perturbacji homotopii
HPM
homotopijna metoda perturbacyjna
oscylator Van der Pol-Duffing
analiza stabilności
teoria perturbacji
oscylator nieliniowy
analiza częstotliwościowa
Opis:
In this paper, we perform the frequency-expansion formula for the nonlinear cubic damping van der Pol’s equation, and the nonlinear frequency is derived. Stability conditions are performed, for the first time ever, by the nonlinear frequency technology and for the nonlinear oscillator. In terms of the van der Pol’s coefficients the stability conditions have been performed. Further, the stability conditions are performed in the case of the complex damping coefficients. Moreover, the study has been extended to include the influence of a forcing van der Pol’ oscillator. Stability conditions have been derived at each resonance case. Redoing the perturbation theory for the van der Pol oscillator illustrates more of a resonance formulation such as sub-harmonic resonance and super-harmonic resonance. More approximate nonlinear dispersion relations of quartic and quintic forms in the squaring of the extended frequency are derived, respectively.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 3; 31-44
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the homotopy perturbation method for the systems of Fredholm integral equations
Zastosowanie homotopijnej metody perturbacyjnej do układów równań całkowych typu Fredholma
Autorzy:
Hetmaniok, E.
Słota, D.
Wróbel, A.
Zielonka, A.
Powiązania:
https://bibliotekanauki.pl/articles/87304.pdf
Data publikacji:
2015
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
homotopijna metoda perturbacyjna
konwergencja
szacowanie błędu
równanie całkowe
homotopy perturbation method
convergence
error estimation
integral equation
Opis:
In this paper the convergence of homotopy perturbation method for the systems of Fredholm integral equations of the second kind is proved. Estimation of errors of approximate solutions obtained by taking the partial sum of the series is also elaborated in the paper.
W artykule wykazano zbieżność homotopijnej metody perturbacyjnej dla układów równań całkowych Fredholma drugiego rodzaju. Podano także oszacowanie błędu rozwiązania przybliżonego uzyskanego jako suma częściowa tworzonego w metodzie szeregu.
Źródło:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska; 2015, 5; 61-70
2084-073X
Pojawia się w:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the homotopy perturbation method for the systems of Volterra integral equations
Zastosowanie homotopijnej metody perturbacyjnej do układów równań całkowych typu Volterry
Autorzy:
Hetmaniok, E.
Słota, D.
Wróbel, A.
Zielonka, A.
Powiązania:
https://bibliotekanauki.pl/articles/87306.pdf
Data publikacji:
2015
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
homotopijna metoda perturbacyjna
konwergencja
szacowanie błędu
równanie całkowe
homotopy perturbation method
convergence
error estimation
integral equation
Opis:
In this paper the convergence of homotopy perturbation method for the systems of Volterra integral equations of the second kind is proved. Estimation of errors of approximate solutions obtained by taking the partial sum of the series is also elaborated in the paper.
W artykule wykazano zbieżność homotopijnej metody perturbacyjnej dla układów równań całkowych Volterry drugiego rodzaju. Podano także oszacowanie błędu rozwiązania przybliżonego uzyskanego jako suma częściowa tworzonego w metodzie szeregu.
Źródło:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska; 2015, 5; 71-77
2084-073X
Pojawia się w:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Homotopy perturbation method combined with Trefftz method in numerical identification of liquid temperature in flow boiling
Autorzy:
Hożejowska, S.
Powiązania:
https://bibliotekanauki.pl/articles/281648.pdf
Data publikacji:
2015
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
homotopy perturbation method
Trefftz method
flow boiling
inverse problem
Opis:
The paper is focused on numerical identification of 2D temperature fields in flow boiling of the liquid through a horizontal minichannel with a rectangular cross-section. The heat transfer process in the minichannel is described by a two-dimensional energy equation with the corresponding boundary conditions. Liquid temperature is determined using the homotopy perturbation method (HPM) with Trefftz functions for Laplace’a equation. The numerical solution to the energy equation found with the HPM is compared with the solution obtained for the simplified form of the energy equation. Considering that only the thermal sublayer is taken into account, both solutions give similar results.
Źródło:
Journal of Theoretical and Applied Mechanics; 2015, 53, 4; 969-980
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Thermal performance of porous fins with temperature-dependent heat generation via the homotopy perturbation method and collocation method
Autorzy:
Hoshyar, H. A.
Rahimipetroudi, I.
Ganji, D. D.
Majidian, A. R.
Powiązania:
https://bibliotekanauki.pl/articles/122933.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
collocation method
homotopy perturbation method
porous fin
temperature-dependent heat generation
Opis:
An analysis has been performed to study the problem of the thermal performance of a nonlinear problem of the porous fin with temperature-dependent internal heat generation. Highly accurate semi-analytical methods called the collocation method (CM) and the homotopy perturbation method (HPM) are introduced and then are used to obtain a nonlinear temperature distribution equation in a longitudinal porous fin. This study is performed using passage velocity from the Darcy’s model to formulate the heat transfer equation through porous media. The heat generation is assumed to be a function of temperature. The effects of the natural convection parameter Nc, internal heat generation εg, porosity Sh and generation number G parameter on the dimensionless temperature distribution are discussed. Also, numerical calculations called the fourth order Runge-Kutta method were carried out for the various parameters entering into the problem for validation. Results reveal that analytical approaches are very effective and convenient. Also it is found that these methods can achieve more suitable results compared to numerical methods.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 4; 53-65
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An analytical technique for solving general linear integral equations of the second kind and its application in analysis of flash lamp control circuit
Autorzy:
Hetmaniok, E.
Słota, D.
Trawiński, T.
Wituła, R.
Powiązania:
https://bibliotekanauki.pl/articles/201450.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
homotopy perturbation method
integral equation
convergence
error estimation
Opis:
In this paper an application of the homotopy perturbation method for solving the general linear integral equations of the second kind is discussed. It is shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in the homotopy perturbation method is convergent. The error of approximate solution, received by taking only the partial sum of the series, is also estimated. Moreover, there is presented an example of applying the method for approximate solution of an equation which has a practical application for charge calculation in supply circuit of the flash lamps used in cameras.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 3; 413-421
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical solutions of electro-kinetic flow in nano-fluidic components by using He’s homotopy perturbation method
Analityczne rozwiązania uzyskane perturbacyjną metodą homotopii He’go dla elektrokinetycznego przepływu przez nano-struktury
Autorzy:
Khaki, M.
Taeibi-Rahni, M.
Ganji, D. D.
Powiązania:
https://bibliotekanauki.pl/articles/949178.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
electro-kinetic flow
nanochannels
homotopy perturbation method (HPM)
Opis:
This paper aims to examine the electro-kinetic flow through nano-channels. The equations governing the fluid flow in a one dimensional channel are derived from the Poisson-Nernst-Planck theory. The boundary conditions for the governing equations are obtained from the electrochemical equilibrium requirements. The coupled equations are transformed into a single differential equation. The transformed equation is solved by He’s homotopy perturbation method and an exact solution is achieved. The validity of results is verified by comparing with existing numerical results. The results are presented for velocity profiles, electrical potential distributions, mole fraction of cation and anion distributions and other physical properties. The results demonstrate reasonable agreement with those provided by other numerical methods and good accuracy of the obtained analytical solutions.
Celem pracy jest przedstawienie wyników badań nad elektrokinetycznym przepływem cieczy przez nano-kanały. Równania opisujące przepływ w jednowymiarowym kanale wyprowadzono na podstawie teorii Poissona-Nernsta-Plancka. Warunki brzegowe uzyskano po spełnieniu wymogów równowagi elektrochemicznej układu. Sprzężone równania przepływu przekształcono do postaci pojedynczego równania różniczkowego. Następnie rozwiązano go za pomocą perturbacyjnej metody homotopii He’go, otrzymując wyrażenie analityczne i dokładne. Poprawność rezultatów sprawdzono, porównując je z istniejącymi wynikami symulacji numerycznych. Zaprezentowano profile prędkości przepływu, rozkłady potencjału elektrycznego, molowe udziały frakcji anionów i kationów oraz inne parametry fizyczne układu. Wszystkie wyniki wykazały dobrą zgodność z obliczeniami opartymi na innych metodach badawczych, co potwierdziło dokładność otrzymanych rozwiązań analitycznych.
Źródło:
Journal of Theoretical and Applied Mechanics; 2013, 51, 2; 265-274
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
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