فهرس المقالات Homotopy Analysis Method

• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  1 - رویکردی نوین در بکارگیری روش تحلیل هموتوپی
  مجتبی قنبری
  10.30495/jnrm.2022.61409.2106
  یکی از روش های بسیار مهم در حل مسائل خطی و غیرخطی، روش تحلیل هموتوپی است که توسط لیائو در سال 1992 مطرح گردید. هدف اصلی این مقاله، بهبود روش تحلیل هموتوپی است که این نوع بهبود یافته را روش تحلیل هموتوپی متوالی نامگذاری نموده ایم. جهت مقایسه ی نتایج به دست آمده توسط روش أکثر

  یکی از روش های بسیار مهم در حل مسائل خطی و غیرخطی، روش تحلیل هموتوپی است که توسط لیائو در سال 1992 مطرح گردید. هدف اصلی این مقاله، بهبود روش تحلیل هموتوپی است که این نوع بهبود یافته را روش تحلیل هموتوپی متوالی نامگذاری نموده ایم. جهت مقایسه ی نتایج به دست آمده توسط روش تحلیل هموتوپی و نوع متوالی آن، چندین مثال عددی ارائه شده است که نتایج نشان می دهند، حجم محاسبات در روش تحلیل هموتوپی متوالی نسبت به نوع معمولی آن کمتر است. همچنین، برخلاف روش تحلیل هموتوپی، جواب های عددی به دست آمده توسط روش تحلیل هموتوپی متوالی در یک محدوده ی نسبتاً وسیعی رضایتبخش هستند. بنابراین، با توجه به روش تحلیل هموتوپی متوالی، می توان انواع مختلف معادلات ریاضی خطی و غیرخطی و همچنین معادلاتی غیر خطی که در سایر رشته های علمی مانند فیزیک و مکانیک به وجود می آیند را به صورت عددی حل نمود. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  2 - Semi-analytical ‎M‎ethod to Solve the Non-linear System of Equations to Model of Evolution for Smoking Habit in ‎Spain
  S. Noeiaghdam K. Kamal Ali
  An epidemiological model of smoking habit is studied by using one of flexible and accurate semi-analytical methods. For this reason, the homotopy analysis transform method (HATM) is applied. Convergence theorem is studied and several h-curves are demonstrated to show th أکثر

  An epidemiological model of smoking habit is studied by using one of flexible and accurate semi-analytical methods. For this reason, the homotopy analysis transform method (HATM) is applied. Convergence theorem is studied and several h-curves are demonstrated to show the convergence regions. Also, the optimal convergence regions are obtained by demonstrating the residual error functions versus h. The numerical tables are presented to show the precision of method. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  3 - Solution of fuzzy differential equations
  M. Otadi M. Mosleh
  Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎The hybrid differential equations have a wide range of applications in science and engineering‎. ‎The hybrid systems are devoted to modeling‎, ‎desig أکثر

  Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎The hybrid differential equations have a wide range of applications in science and engineering‎. ‎The hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎Hybrid fuzzy differential equations (HFDEs) is considered by Kim et al.‎ [11]. ‎In the present paper it is shown that the example presented by Kim et al‎. ‎in the Case I is not very accurate and in the Case II‎, ‎is incorrect.‎ ‎Namely‎, ‎the exact solution proposed by the authors in the Case II are not solutions of the given HFDE‎. ‎The correct exact solution is also presented here‎, ‎together with some results for characterizing solutions of FDEs under‎ ‎Hukuhara differentiability by an equivalent system of ODEs‎. ‎Then‎, ‎the homotopy analysis method (HAM) is applied to obtained the series solution of the HFDEs‎. ‎Finally‎, ‎we illustrate‎ ‎our approach by a numerical ‎example.‎ تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  4 - Homotopy approximation technique for solving nonlinear‎ ‎Volterra-Fredholm integral equations of the first kind
  SH. Sadigh ‎Behzadi
  In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The app أکثر

  In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy of the proposed numerical scheme is examined by comparing with other analytical and numerical results. The existence, uniqueness and convergence of the proposed method are proved. Example is presented to illustrate the efficiency and the performance of the homotopy analysis ‎method.‎ تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  5 - On convergence of homotopy analysis method to solve the Schrodinger equation with a power law nonlinearity
  M. A. Fariborzi Araghi S. Naghshband
  In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also أکثر

  In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the eciency of the mentioned algorithm and theh-curve is plotted to determine the region of convergence. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  6 - Nonlinear Vibration Analysis of FG Nano-Beams in Thermal Environment and Resting on Nonlinear Foundation based on Nonlocal and Strain-Inertia Gradient Theory
  Ebrahim Mahmoudpour
  In present research, nonlinear vibration of functionally graded nano-beams subjected to uniform temperature rise and resting on nonlinear foundation is comprehensively studied. The elastic center can be defined to remove stretching and bending couplings caused by the FG أکثر

  In present research, nonlinear vibration of functionally graded nano-beams subjected to uniform temperature rise and resting on nonlinear foundation is comprehensively studied. The elastic center can be defined to remove stretching and bending couplings caused by the FG material variation. The small-size effect, playing essential role in the dynamical behavior of nano-beams, is considered here applying strain-inertia gradient and non-local elasticity theory. The governing partial differential equations have been derived based on the Euler-Bernoulli beam theory utilizing the von Karman strain-displacement relations. Subsequently, using the Galerkin method, the governing equations is reduced to a nonlinear ordinary differential equation. The closed form analytical solution of the nonlinear natural frequency is then established using the homotopy analysis method. Finally, the effects of different parameters such as length, nonlinear elastic foundation parameter, thermal loading, non-local parameter and gradient parameters are comprehensively investigated on the FG nano-beams vibration using homotopy analysis method. As the main results, it is observed that by increasing the non-local parameter, the frequency ratio for strain-inertia gradient theory has increasing trend while it has decreasing trend for non-local elasticity theory. Also, the nonlinear natural frequencies obtained using strain-inertia gradient theory are greater than the results of non-local elasticity and classical theory. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  7 - Nonlinear Nonlocal Vibration of an Embedded Viscoelastic Y-SWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method
  A Ghorbanpour Arani M.Sh Zarei
  In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Y-shaped single walled carbon nanotube (Y-SWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The Y-SWCNT is also subjected to a أکثر

  In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Y-shaped single walled carbon nanotube (Y-SWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The Y-SWCNT is also subjected to a longitudinal magnetic field which produces Lorentz force in transverse direction. In order to consider the small scale effects, nonlocal elasticity theory is applied due to its simplicity and accuracy. The small-size effects and slip boundary conditions of nano-flow are taken into account through Knudsen number (Kn). The Y-SWCNT is surrounded by elastic medium which is simulated as nonlinear Visco-Pasternak foundation. Using energy method and Hamilton’s principle, the nonlinear governing motion equation is obtained. The governing motion equation is solved using both Galerkin procedure and Homotopy analysis method (HAM). Numerical results indicate the significant effects of the mass and velocity of the fluid flow, strength of longitudinally magnetic field, (Kn), angle between the centerline of carbon nanotube and the downstream elbows, nonlocal parameter and nonlinear Visco-Pasternak elastic medium. The results of this work is hoped to be of use in design and manufacturing of nano-devices in which Y-shaped nanotubes act as basic elements. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  8 - Vibration Analysis of a Nonlinear Beam Under Axial Force by Homotopy Analysis Method
  A.A Motallebi M Poorjamshidian J Sheikhi
  In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is us أکثر

  In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differential equation. Then Homotopy Analysis Method is employed to obtain an analytic expression for nonlinear natural frequencies. Effects of design parameters including axial force and slenderness ratio on nonlinear natural frequencies are studied. Moreover, effects of factors of nonlinear terms on the general shape of the time response are taken into account. Combined Homotopy-Pade technique is used to reduce the number of approximation orders without affecting final accuracy. The results indicate increased speed of convergence as Homotopy and Pade are combined. The obtained analytic expressions can be used for a vast range of data. Comparison of the results with numerical data indicated a good conformance. Having compared accuracy of this method with that of the Homotopy perturbation analytic method, it is concluded that Homotopy Analysis Method is a very strong method for analytic and vibration analysis of structures. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  9 - Some notes on convergence of homotopy based methods for functional equations
  A Azizi J Saeidian E Babolian
  Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergenc أکثر

  Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizing previous works, a sucient condition for convergence ofhomotopy methods is presented. Finally, examples are given to show that evenif the homotopy method leads to a convergent series, it may not converge tothe exact solution of the equation under consideration. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  10 - Some notes on convergence of homotopy based methods for functional equations
  A. Azizi J. Saiedian E. Babolian
  Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergenc أکثر

  Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizing previous works, a sucient condition for convergence ofhomotopy methods is presented. Finally, examples are given to show that evenif the homotopy method leads to a convergent series, it may not converge tothe exact solution of the equation under consideration. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  11 - Some notes concerning the convergence control parameter in homotopy analysis method
  M. Paripour J. Saeidian
  omotopy analysis method (HAM) is a promising method for handling func-tional equations. Recent publications proved the eectiveness of HAM in solvingwide variety of problems in dierent elds. HAM has a unique property whichmakes it superior to other analytic methods, t أکثر

  omotopy analysis method (HAM) is a promising method for handling func-tional equations. Recent publications proved the eectiveness of HAM in solvingwide variety of problems in dierent elds. HAM has a unique property whichmakes it superior to other analytic methods, this property is its ability to con-trol the convergence region of the solution series. In this work, we claried theadvantages and eects of convergence-control parameter through an example. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  12 - Numerical solution of fuzzy Hunter-Saxton equation by using Adomian decomposition and Homotopy analysis methods
  Sh Sadigh behzadi
  In this paper, a fuzzy Hunter-Saxton equation is solved by using the Adomian'sdecomposition method (ADM) and homotopy analysis method (HAM). Theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a rec أکثر

  In this paper, a fuzzy Hunter-Saxton equation is solved by using the Adomian'sdecomposition method (ADM) and homotopy analysis method (HAM). Theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. The existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. A numerical example is studied to demonstrate the accuracy ofthe presented methods.In this paper, a fuzzy Hunter-Saxton equation is solved by using the Adomian'sdecomposition method (ADM) and homotopy analysis method (HAM). Theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. The existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. A numerical example is studied to demonstrate the accuracy ofthe presented methods. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  13 - Multiple solutions of the nonlinear reaction-di usion model with fractional reaction
  H. Vosoughi E. Shivanian M. Anbarloei
  The purpose of this letter is to revisit the nonlinear reaction-diusion modelin porous catalysts when reaction term is fractional function of the concen-tration distribution of the reactant. This model, which originates also in uidand solute transport in soft tissues a أکثر

  The purpose of this letter is to revisit the nonlinear reaction-diusion modelin porous catalysts when reaction term is fractional function of the concen-tration distribution of the reactant. This model, which originates also in uidand solute transport in soft tissues and microvessels, has been recently givenanalytical solution in terms of Taylors series for dierent family of reactionterms. We apply the method so-called predictor homotopy analysis method(PHAM) which has been recently proposed to predict multiplicity of solutionsof nonlinear BVPs. Consequently, it is indicated that the problem for somevalues of the parameter admits multiple solutions. Also, error analysis of thesesolutions are given graphically. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  14 - Application of Numerical Iterative Methods for Solving Benjamin-Bona-Mahony Equation
  Shadan Sadigh behzadi
  In this paper, a generalized Benjamin-Bona-Mahony equation ( BBM)is solved by using the Adomian's decomposition method (ADM) ,modified Adomian's decomposition method (MADM), variationaliteration method (VIM), modified variational iteration method (MVIM)and homotopy anal أکثر

  In this paper, a generalized Benjamin-Bona-Mahony equation ( BBM)is solved by using the Adomian's decomposition method (ADM) ,modified Adomian's decomposition method (MADM), variationaliteration method (VIM), modified variational iteration method (MVIM)and homotopy analysis method (HAM). The approximate solution of thisequation is calculated in the form of series which its componentsare computed by applying a recursive relation. The existence anduniqueness of the solution and the convergence of the proposedmethods are proved. A numerical example is studied to demonstratethe accuracy of the presented methods.The MVIM has been shown to solve effectively, easily and accuratelya large class of nonlinear problems with the approximations whichconvergent are rapidly to exact solutions. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  15 - Solving Nonlinear Klein-Gordon Equation with a Quadratic Nonlinear term using Homotopy Analysis Method
  H. جعفری م. سعیدی م. عرب فیروزجایی
  In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method أکثر

  In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  16 - Analytic-Approximate Solution For An Integro- Differential Equation Arising In Oscillating Magnetic Fields Using Homotopy Analysis Method
  H. صابری نیک S. عفتی ر. بوژآبادی
  In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving th أکثر

  In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity and efficiency of this method. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  17 - A note on the convergence of the Zakharov-Kuznetsov equation by homotopy analysis method
  A. Fallahzadeh M. A. Fariborzi Araghi
  In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homotopy analysis method (HAM) is investigated. A theorem is proved to guarantee the convergence of HAM and to find the series solution of this equation via a reliable algorithm.

  In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homotopy analysis method (HAM) is investigated. A theorem is proved to guarantee the convergence of HAM and to find the series solution of this equation via a reliable algorithm. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  18 - On the convergence of the homotopy analysis method to solve the system of partial differential equations
  A. Fallahzadeh M. A. Fariborzi Araghi V. Fallahzadeh
  One of the efficient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (HAM). In this work, we obtain the approximate solution ofa system of partial differential equations (PDEs) by means of HAM. For this purpose, wedevelop the conc أکثر

  One of the efficient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (HAM). In this work, we obtain the approximate solution ofa system of partial differential equations (PDEs) by means of HAM. For this purpose, wedevelop the concept of HAM for a system of PDEs as a matrix form. Then, we prove theconvergence theorem and apply the proposed method to defined the approximate solution ofsome systems of PDEs. Also, we show the region of convergence by plotting the H-surface. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  19 - An Efficient Method to Solve the Mathematical Model of HIV Infection for CD8+ T-Cells
  Samad Noeiaghdam Emran Khoshrouye Ghiasi
  In this paper, the mathematical model of HIV infection forCD8+ T-cells is illustrated. The homotopy analysis method and the Laplace transformations are combined for solving this model. Also, the convergence theorem is proved to demonstrate the abilities of presented met أکثر

  In this paper, the mathematical model of HIV infection forCD8+ T-cells is illustrated. The homotopy analysis method and the Laplace transformations are combined for solving this model. Also, the convergence theorem is proved to demonstrate the abilities of presented method for solving non-linear mathematical models. The numerical results for $N=5, 10$ are presented. Several $hbar$-curves are plotted to show the convergence regions of solutions. The plots of residual error functions indicate the precision of presented method. تفاصيل المقالة
• حرية الوصول المقاله
  • صفحة الملخص
  • نص كامل
  
  20 - NUMERICAL SOLUTION OF BOUSSINESQ EQUATION USING MODIFIED ADOMIAN DECOMPOSITION AND HOMOTOPY ANALYSIS METHODS
  Sh. Sadigh Behzadi
  In this paper, a Boussinesq equation is solved by using the Adomian's decomposition method, modified Adomian's decomposition method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its components are compu أکثر

  In this paper, a Boussinesq equation is solved by using the Adomian's decomposition method, modified Adomian's decomposition method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved in detail. A numerical example is studied to demonstrate the accuracy of the presented methods. تفاصيل المقالة