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Journal articles on the topic 'Variational asymptotic method'

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Published: 4 June 2021

Last updated: 6 September 2023

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1

NICODEMUS, ROLF, S. GROSSMANN, and M. HOLTHAUS. "The background flow method. Part 2. Asymptotic theory of dissipation bounds." Journal of Fluid Mechanics 363 (May 25, 1998): 301–23. http://dx.doi.org/10.1017/s0022112098001177.

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We study analytically the asymptotics of the upper bound on energy dissipation for the two-dimensional plane Couette flow considered numerically in Part 1 of this work, in order to identify the mechanisms underlying the variational approach. With the help of shape functions that specify the variational profiles either in the interior or in the boundary layers, it becomes possible to quantitatively explain all numerically observed features, from the occurrence of two branches of minimizing wavenumbers to the asymptotic parameter scaling with the Reynolds number. In addition, we derive a new var

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2

He, Ji-Huan. "Asymptotic Methods for Solitary Solutions and Compactons." Abstract and Applied Analysis 2012 (2012): 1–130. http://dx.doi.org/10.1155/2012/916793.

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This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variatio

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3

Sutyrin, V. G. "Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation." Journal of Applied Mechanics 64, no. 4 (1997): 905–15. http://dx.doi.org/10.1115/1.2788998.

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The focus of this paper is the development of linear, asymptotically correct theories for inhomogeneous orthotropic plates, for example, laminated plates with orthotropic laminae. It is noted that the method used can be easily extended to develop nonlinear theories for plates with generally anisotropic inhomogeneity. The development, based on variational-asymptotic method, begins with three-dimensional elasticity and mathematically splits the analysis into two separate problems: a one-dimensional through-the-thickness analysis and a two-dimensional “plate” analysis. The through-the-thickness a

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4

Gottwald, Georg A., and Marcel Oliver. "Slow dynamics via degenerate variational asymptotics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2170 (2014): 20140460. http://dx.doi.org/10.1098/rspa.2014.0460.

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We introduce the method of degenerate variational asymptotics for a class of singularly perturbed ordinary differential equations in the limit of strong gyroscopic forces. Such systems exhibit dynamics on two separate time scales. We derive approximate equations for the slow motion to arbitrary order through an asymptotic expansion of the Lagrangian in suitably transformed coordinates. We prove that the necessary near-identity change of variables can always be constructed and that solutions of the slow limit equations shadow solutions of the full parent model at the expected order over a finit

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5

HE, JI-HUAN. "SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS." International Journal of Modern Physics B 20, no. 10 (2006): 1141–99. http://dx.doi.org/10.1142/s0217979206033796.

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This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are e

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6

YARMUKHAMEDOV, R., та M. K. UBAYDULLAEVA. "ON ASYMPTOTICS OF THREE-BODY BOUND STATE RADIAL WAVE FUNCTIONS OF HALO NUCLEI NEAR THE HYPERANGLE φ~0 AND φ~π/2 IN THE CONFIGURATION SPACE AND THREE-BODY ASYMPTOTIC NORMALIZATION FACTORS FOR 6He NUCLEUS IN THE (n+n+α)-CHANNEL". International Journal of Modern Physics E 18, № 07 (2009): 1561–85. http://dx.doi.org/10.1142/s0218301309013701.

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Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π

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7

Baranwal, Vipul K., Ram K. Pandey, and Om P. Singh. "Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations." International Scholarly Research Notices 2014 (October 15, 2014): 1–12. http://dx.doi.org/10.1155/2014/847419.

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We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ0,γ1,γ2,… and auxiliary functions H0(x),H1(x),H2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source

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8

Sachdeva, Chirag, and Srikant S. Padhee. "Analysis of Bidirectionally Graded Cylindrical Beams Using Variational Asymptotic Method." AIAA Journal 57, no. 10 (2019): 4169–81. http://dx.doi.org/10.2514/1.j057562.

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9

Shibata, Tetsutaro. "Variational method for precise asymptotic formulas for nonlinear eigenvalue problems." Results in Mathematics 46, no. 1-2 (2004): 130–45. http://dx.doi.org/10.1007/bf03322876.

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10

Li, Xi, and Da-ming Yuan. "Asymptotic approximation method for elliptic variational inequality of first kind." Applied Mathematics and Mechanics 35, no. 3 (2014): 381–90. http://dx.doi.org/10.1007/s10483-014-1798-x.

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11

Pavan, G. S., S. Keshava Kumar, and K. S. Nanjunda Rao. "Bending analysis of laminated beams using isogeometric variational asymptotic method." International Journal of Advances in Engineering Sciences and Applied Mathematics 12, no. 1-2 (2020): 27–38. http://dx.doi.org/10.1007/s12572-020-00264-8.

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12

HE, JI-HUAN. "AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING." International Journal of Modern Physics B 22, no. 21 (2008): 3487–578. http://dx.doi.org/10.1142/s0217979208048668.

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This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-infinity theory in high energy physics, Kleiber's 3/4 law in biology, possible mechanism in spider-spinning process and fracta

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13

Narayana, K. Jagath, Ramesh Gupta Burela, Sathiskumar Anusuya Ponnusami, and Dineshkumar Harursampath. "Geometric Nonlinear Analysis of Composite Stiffened Panels Using Variational Asymptotic Method." AIAA Journal 58, no. 9 (2020): 4189–203. http://dx.doi.org/10.2514/1.j058963.

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14

Yu, Wenbin, and Tian Tang. "Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials." International Journal of Solids and Structures 44, no. 11-12 (2007): 3738–55. http://dx.doi.org/10.1016/j.ijsolstr.2006.10.020.

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15

WEI, BO-BO. "TWO ONE-DIMENSIONAL INTERACTING PARTICLES IN A HARMONIC TRAP." International Journal of Modern Physics B 23, no. 18 (2009): 3709–15. http://dx.doi.org/10.1142/s0217979209053345.

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In this brief report, two one-dimensional interacting particles interacting with a delta interaction in a harmonic trap is discussed. For strong interactions, we derive the asymptotic expressions for all the energy levels. In addition, the variational method is used to obtain asymptotic ground state energy and wave function. The variational results are compared with the exact solution and they turn out to agree very well.

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16

Fulmański, Piotr, Antoine Laurain, Jean-Francois Scheid, and Jan Sokołowski. "A Level Set Method in Shape and Topology Optimization for Variational Inequalities." International Journal of Applied Mathematics and Computer Science 17, no. 3 (2007): 413–30. http://dx.doi.org/10.2478/v10006-007-0034-z.

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A Level Set Method in Shape and Topology Optimization for Variational InequalitiesThe level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations

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17

Kamineni, Jagath Narayana, and Ramesh Gupta Burela. "Constraint method for laminated composite flat stiffened panel analysis using variational asymptotic method (VAM)." Thin-Walled Structures 145 (December 2019): 106374. http://dx.doi.org/10.1016/j.tws.2019.106374.

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18

ZAREMBO, K. "RENORMALIZATION OF FUNCTIONAL SCHRÖDINGER EQUATION BY BACKGROUND FIELD METHOD." Modern Physics Letters A 13, no. 21 (1998): 1709–17. http://dx.doi.org/10.1142/s0217732398001789.

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Renormalization group transformations for Schrödinger equation are performed in both φ4 and Yang–Mills theories. The dependence of the ground state wave functional on rapidly oscillating fields is found. For Yang–Mills theory, this dependence restricts a possible form of variational ansatz compatible with asymptotic freedom.

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19

Keshava Kumar, S. "Review of Laminated Composite Plate Theories, with Emphasis on Variational Asymptotic Method." AIAA Journal 57, no. 10 (2019): 4182–88. http://dx.doi.org/10.2514/1.j057552.

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20

Kumar, Dileep, and Dineshkumar Harursampath. "Application of Variational Asymptotic Micromechanical Method to Strength Analysis of Composite Materials." Key Engineering Materials 801 (May 2019): 95–100. http://dx.doi.org/10.4028/www.scientific.net/kem.801.95.

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One of the most important features of a material to know before using it is the maximum limit of the load at which it fails. This paper presents a micromechanical strength theory to estimate the tensile strength of the unidirectional fiber reinforced composite. The fibers used can be considered transversely isotropic and elastic till failure, but the matrix material is considered to be Elastic-plastic. The mathematical formulation used is the Variational-Asymptotic Method (VAM), which is used to construct the asymptotically-correct a reduced-dimensional model that is free of a priori assumptio

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21

Ali, Javed, S. Islam, Hamid Khan, and Syed Inayat Ali Shah. "The Optimal Homotopy Asymptotic Method for the Solution of Higher-Order Boundary Value Problems in Finite Domains." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/401217.

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We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM). The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM), variational iteration (VIM), homotopy perturbation (HPM), and variational iteration decomposition method (VIDM). The results show that the proposed method is more effective and reliable.

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22

BETTINSON, DAVID C., and GEORGE ROWLANDS. "Transverse stability of plane solitons using the variational method." Journal of Plasma Physics 59, no. 3 (1998): 543–54. http://dx.doi.org/10.1017/s0022377898006448.

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We present stability results for plane soliton solutions of two versions of the two-dimensional KdV equation, namely the Zakharov–Kuznetsov (ZK) equation and the Kadomtsev–Petviashvili equation for positive dispersion (KP+ equation). To do this we use a linear variation-of-action method (VAM). Others have used this method, but with little success when applied to these two equations. The best results have given the correct instability range, but the predicted growth rates have significant errors. For the ZK equation we show, by paying more attention to the spatially asymptotic form of the trial

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23

Ali, Shah, Imtiaz Ahmad, Hanaa Abu-Zinadah, Khedher Mohamed, and Hijaz Ahmad. "Multistage optimal homotopy asymptotic method for the K(2,2) equation arising in solitary waves theory." Thermal Science 25, Spec. issue 2 (2021): 199–205. http://dx.doi.org/10.2298/tsci21s2199a.

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The paper is concern to the approximate analytical solution of K(2,2) using the multistage homotopy asymptotic method which are used in modern physics and engineering. The suggested algorithm is an accurate, effective, and simple to-utilize semi-analytic tool for non-linear problems, and in this manner the current investigation highlights the efficiency and accuracy of the method for the solution of non-linear PDE for large time span. Numerical comparison with the variational iteration method and with homotopy asymptotic method shows the efficacy and accuracy of the proposed method.

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24

NICODEMUS, ROLF, S. GROSSMANN, and M. HOLTHAUS. "The background flow method. Part 1. Constructive approach to bounds on energy dissipation." Journal of Fluid Mechanics 363 (May 25, 1998): 281–300. http://dx.doi.org/10.1017/s0022112098001165.

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We present a numerical strategy that allows us to explore the full scope of the Doering–Constantin variational principle for computing rigorous upper bounds on energy dissipation in turbulent shear flow. The key is the reformulation of this principle's spectral constraint as a boundary value problem that can be solved efficiently for all Reynolds numbers of practical interest. We state results obtained for the plane Couette flow, and investigate in detail a simplified model problem that can serve as a definite guide for the application of the variational principle to other flows. The most nota

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25

BENCHETTAH, DJABER CHEMSEDDINE. "L ∞−ASYMPTOTIC BEHAVIOR OF A FINITE ELEMENT METHOD FOR A SYSTEM OF PARABOLIC QUASI-VARIATIONAL INEQUALITIES WITH NONLINEAR SOURCE TERMS." Kragujevac Journal of Mathematics 47, no. 3 (2023): 347–67. http://dx.doi.org/10.46793/kgjmat2303.347b.

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This paper is an extension and a generalization of the previous results, cf. [3, 6, 8, 11]. It is devoted to studying the finite element approximation of the non coercive system of parabolic quasi-variational inequalities related to the management of energy production problem. Specifically, we prove optimal L∞-asymptotic behavior of the system of evolutionary quasi-variational inequalities with nonlinear source terms using the finite element spatial approximation and the subsolutions method

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26

Nawaz, R., S. Islam, I. A. Shah, M. Idrees, and H. Ullah. "Optimal Homotopy Asymptotic Method to Nonlinear Damped Generalized Regularized Long-Wave Equation." Mathematical Problems in Engineering 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/503137.

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A new semianalytical technique optimal homology asymptotic method (OHAM) is introduced for deriving approximate solution of the homogeneous and nonhomogeneous nonlinear Damped Generalized Regularized Long-Wave (DGRLW) equation. We tested numerical examples designed to confine the features of the proposed scheme. We drew 3D and 2D images of the DGRLW equations and the results are compared with that of variational iteration method (VIM). Results reveal that OHAM is operative and very easy to use.

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27

LI, XIAOLIN. "THE MESHLESS GALERKIN BOUNDARY NODE METHOD FOR TWO-DIMENSIONAL SOLIDS." International Journal of Computational Methods 10, no. 04 (2013): 1350013. http://dx.doi.org/10.1142/s0219876213500138.

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The Galerkin boundary node method (GBNM) is developed for two-dimensional solid mechanics problems. The GBNM is a boundary only meshless method that combines an equivalent variational form of boundary integral formulations for governing equations with the moving least-squares (MLS) approximations for construction of the trial and test functions. In this method, boundary conditions can be implemented directly and easily despite the MLS shape functions lack the delta function property, and the resulting formulation inherits the symmetry and positive definiteness of the variational problems. The

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28

Ghorashi, Mehrdaad. "Nonlinear static and stability analysis of composite beams by the variational asymptotic method." International Journal of Engineering Science 128 (July 2018): 127–50. http://dx.doi.org/10.1016/j.ijengsci.2018.03.011.

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29

Geng, Fazhan, Suping Qian, and Shuai Li. "Numerical solutions of singularly perturbed convection-diffusion problems." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 6 (2014): 1268–74. http://dx.doi.org/10.1108/hff-01-2013-0033.

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Purpose – The purpose of this paper is to find an effective numerical method for solving singularly perturbed convection-diffusion problems. Design/methodology/approach – The present method is based on the asymptotic expansion method and the variational iteration method (VIM). First a zeroth order asymptotic expansion for the solution of the given singularly perturbed convection-diffusion problem is constructed. Then the reduced terminal value problem is solved by using the VIM. Findings – Two numerical examples are introduced to show the validity of the present method. Obtained numerical resu

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30

Ullah, Hakeem, Saeed Islam, Muhammad Idrees, Mehreen Fiza, and Zahoor Ul Haq. "An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation." International Journal of Differential Equations 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/106934.

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We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM). We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM) and homotopy perturbation method (HPM) solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

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31

Ponte Castan˜eda, P. "Plastic Stress Intensity Factors in Steady Crack Growth." Journal of Applied Mechanics 54, no. 2 (1987): 379–87. http://dx.doi.org/10.1115/1.3173023.

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The asymptotic stress and deformation fields of a crack propagating steadily and quasi-statically into an elastic-plastic material, characterized by J2-flow theory with linear strain-hardening, were first determined by Amazigo and Hutchinson (1977) for the cases of mode III and mode I (plane strain and plane stress). Their solutions were approximate in that they neglected the possibility of plastic reloading on the crack faces. This effect was taken into account by Ponte Castan˜eda (1987b), who also introduced a new formulation for the (eigenvalue) problem in terms of a system of first order O

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32

Yan, Huahong. "Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/735919.

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An adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black-Scholes model is proposed. Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix ordinary differential equations. Next, VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the

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33

Shi, Zheng, Yifeng Zhong, Qingshan Yi, and Xiao Peng. "High efficiency analysis model for composite honeycomb sandwich plate by using variational asymptotic method." Thin-Walled Structures 163 (June 2021): 107709. http://dx.doi.org/10.1016/j.tws.2021.107709.

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34

Zhuk, P. F., and A. A. Musina. "Asymptotic Rate of Convergence of a Two-Layer Iterative Method of the Variational Type." Ukrainian Mathematical Journal 65, no. 12 (2014): 1793–808. http://dx.doi.org/10.1007/s11253-014-0898-7.

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35

Tang, Tian, and Wenbin Yu. "Micromechanical modeling of the multiphysical behavior of smart materials using the variational asymptotic method." Smart Materials and Structures 18, no. 12 (2009): 125026. http://dx.doi.org/10.1088/0964-1726/18/12/125026.

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36

Hodges, Dewey H. "Unified Approach for Accurate and Efficient Modeling of Composite Rotor Blade Dynamics The Alexander A. Nikolsky Honorary Lecture." Journal of the American Helicopter Society 60, no. 1 (2015): 1–28. http://dx.doi.org/10.4050/jahs.60.011001.

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Herein is described the development of a unified approach, which spans several decades and facilitates accurate and efficient modeling of composite helicopter rotor blades for loads, dynamics, aeroelasticity, and stress recovery. The approach achieves accuracy comparable to that of three-dimensional finite element analysis but with significant savings in computational effort. The basis for this approach is a mathematical technique called the variational asymptotic method. This paper summarizes the modeling approach and presents some of the key equations of the resulting analyses. Examples are

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37

Pletzer, A., and R. L. Dewar. "Non-ideal stability: variational method for the determination of the outer-region matching data." Journal of Plasma Physics 45, no. 3 (1991): 427–51. http://dx.doi.org/10.1017/s0022377800015828.

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Within the framework of studies of the stability of magneto-plasmas to non-ideal modes, such as resistive modes, the problem of determining the asymptotic matching data arising from the outer (ideal) region is considered. Modes possessing both tearing and interchange (ballooning) parity are considered in finite-pressure plasmas. The matching data, which form a matrix whose elements represent the small solution response to forcing by a big solution, are shown to derive from a variational (energy) principle. The variational principle, as presented, applies to both cylindrical and two-dimensional

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38

Premoselli, Bruno. "A pointwise finite-dimensional reduction method for a fully coupled system of Einstein–Lichnerowicz type." Communications in Contemporary Mathematics 20, no. 06 (2018): 1750076. http://dx.doi.org/10.1142/s0219199717500766.

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We construct non-compactness examples for the fully coupled Einstein–Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional reductions and a fixed-point argument. More precisely, we perform a fixed-point procedure on the remainders of the expected blow-up decomposition. The argument consists of an involved finite-dimensional reduction coupled with a ping-pong method. To overcome the non-variational structure of the system, we work with remainders which belong to strong function spaces

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39

Fiza, Mehreen, Hakeem Ullah, Saeed Islam, Qayum Shah, Farkhanda Inayat Chohan, and Mustafa Bin Mamat. "Modifications of the Multistep Optimal Homotopy Asymptotic Method to Some Nonlinear KdV-Equations." European Journal of Pure and Applied Mathematics 11, no. 2 (2018): 537–52. http://dx.doi.org/10.29020/nybg.ejpam.v11i2.3194.

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In this article we have introduced the mathematical theory of multistep optimal homotopy asymptotic method (MOHAM). The proposed method is implemented to different models having system of partial differential equations (PDEs). The results obtained by proposed method are compared with Homotopy Analysis Method (HAM) and closed form solutions. The comparisons of these results show that MOHAM is simpler in applicability, effective, explicit, control the convergence through optimal constants, involve less computational work. The MOHAM is independent of the assumption of initial conditions and small

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40

Wang, Fuzhang, Shah Ali, Imtiaz Ahmad, Hijaz Ahmad, Kamran Alam, and Phatiphat Thounthong. "Solution of Burgers’ equation appears in fluid mechanics by multistage optimal homotopy asymptotic method." Thermal Science 26, no. 1 Part B (2022): 815–21. http://dx.doi.org/10.2298/tsci210302343w.

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In this article, we approximate analytical solution of Burgers? equations using the Multistage homotopy asymptotic method which are utilized in modern physics and fluid mechanics. The suggested algorithm is an accurate and simple to-utilize semi-analytic tool for non-linear problems. In the current research we investigation the efficiency and accuracy of the method for the solution of non-linear PDE for large time span. Numerical comparison with the variational iteration method shows the efficacy and accuracy of the proposed method.

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41

Wang, Fuzhang, Ali Shah, Imtiaz Ahmad, Hijaz Ahmad, Kamran Alam, and Phatiphat Thounthong. "Solution of burgers’ equation appears in fluid mechanics by multistage optimal homotopy asymptotic method." Thermal Science 27, Spec. issue 1 (2023): 87–92. http://dx.doi.org/10.2298/tsci23s1087w.

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In this article, we approximate analytical solution of Burgers? equations using the multistage homotopy asymptotic method which are utilized in modern physics and fluid mechanics. The suggested algorithm is an accurate and simple to-utilize semi-analytic tool for non-linear problems. In the current research we investigation the efficiency and accuracy of the method for the solution of non-linear PDE for large time span. Numerical comparison with the variational iteration method shows the efficacy and accuracy of the proposed method.

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42

SISSAKIAN, ALEXEY, IGOR SOLOVTSOV, and OLEG SHEVCHENKO. "VARIATIONAL PERTURBATION THEORY." International Journal of Modern Physics A 09, no. 12 (1994): 1929–99. http://dx.doi.org/10.1142/s0217751x94000832.

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A nonperturbative method — variational perturbation theory (VPT) — is discussed. A quantity we are interested in is represented by a series, a finite number of terms of which not only describe the region of small coupling constant but reproduce well the strong coupling limit. The method is formulated only in terms of the Gaussian quadratures, and diagrams of the conventional perturbation theory are used. Its efficiency is demonstrated for the quantum-mechanical anharmonic oscillator. The properties of convergence are studied for series in VPT for the [Formula: see text] model. It is shown that

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43

Boutarene, Khaled El-Ghaouti. "APPROXIMATE TRANSMISSION CONDITIONS FOR A POISSON PROBLEM AT MID-DIFFUSION." Mathematical Modelling and Analysis 20, no. 1 (2015): 53–75. http://dx.doi.org/10.3846/13926292.2015.1000988.

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This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of RP(P = 2, 3) with a thin layer. We use a method based on hierarchical variational equations to derive an explicitly asymptotic expansion of the solution with respect to the thickness of the thin layer. We determine the first two terms of the expansion and prove the error estimate made by truncating the expansion after a finite number of terms. Next, using the first two terms of the asymptotic expansion, we show that we can model the effect of the thin layer by a problem with transmission co

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44

Colombo, Maria, Luca Spolaor, and Bozhidar Velichkov. "On the asymptotic behavior of the solutions to parabolic variational inequalities." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 768 (2020): 149–82. http://dx.doi.org/10.1515/crelle-2019-0041.

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AbstractWe consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Łojasiewicz inequality. The difficulty lies in the fact that, since the constraint is non-analytic, the pioneering method of L. Simon ([22]) does not apply and we have to exploit a better understanding on the constraint itself. We then apply this inequality to two associated problems. First we combine it with an abstract result on parabolic variational inequalities, to prove the convergence at i

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Décio Jr, R., L. D. Pérez-Fernández, and J. Bravo-Castillero. "Effective Behavior of Nonlinear Microperiodic Composites with Imperfect Contact Via the Asymptotic Homogenization Method." Trends in Computational and Applied Mathematics 22, no. 1 (2021): 79–90. http://dx.doi.org/10.5540/tcam.2021.022.01.00079.

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The asymptotic homogenization method is applied here to one-dimensional boundary-value problems for nonlinear differential equations with rapidly oscillating piecewise-constant coefficients which model the behavior of nonlinear microperiodic composites, in order to assess the influence of interfacial imperfect contact on the effective behavior. In particular, a nonlinear power-law flux on the gradient of the unknown was considered. Several calculations were performed and are discussed at the end of this work, including a comparison of some results with variational ounds, which is also an impor

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MUSZKIETA, MONIKA. "OPTIMAL EDGE DETECTION BY TOPOLOGICAL ASYMPTOTIC ANALYSIS." Mathematical Models and Methods in Applied Sciences 19, no. 11 (2009): 2127–43. http://dx.doi.org/10.1142/s0218202509004066.

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In this paper, we consider a variational approach to the problem of edge detection without using a priori information. To begin with, we derive an asymptotic expansion of a functional inspired by the Mumford–Shah model at its global minimum. Then, we show that, according to our model, the optimal set of image edges is indicated by the set of points for which the dominant term of this expansion is minimal and the topological derivative associated with the considered functional is equal to zero. These two conditions form the basis for the introduced method to edge detection, which does not requi

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Rao, MV Peereswara, K. Renji, and Dineshkumar Harursampath. "Asymptotic theory of 3D thermoelastic stress analysis of honeycomb sandwich panels with composite facesheets." Journal of Sandwich Structures & Materials 22, no. 6 (2018): 1952–82. http://dx.doi.org/10.1177/1099636218791105.

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This work presents an asymptotical thermoelastic model for analyzing symmetric composite sandwich plate structures. Use of three-dimensional finite elements to analyze real-life composite sandwich structures is computationally prohibitive, while use of two-dimensional finite element cannot accurately predict the transverse stresses and three-dimensional displacements. Endeavoring to fill this gap, the present theory is developed based on the variational asymptotic method. The unique features of this work are the identification and utilization of small parameters characterizing the geometry and

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Neto, Maria Augusta, Wenbin Yu, Tian Tang, and Rogério leal. "Analysis and optimization of heterogeneous materials using the variational asymptotic method for unit cell homogenization." Composite Structures 92, no. 12 (2010): 2946–54. http://dx.doi.org/10.1016/j.compstruct.2010.05.006.

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FARROKHZAD, F., P. MOWLAEE, A. BARARI, A. J. CHOOBBASTI, and H. D. KALIJI. "Analytical investigation of beam deformation equation using perturbation, homotopy perturbation, variational iteration and optimal homotopy asymptotic methods." Carpathian Journal of Mathematics 27, no. 1 (2011): 51–63. http://dx.doi.org/10.37193/cjm.2011.01.08.

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The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified, and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy A

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Stanek, Jerzy. "Approximate analytical solutions for arbitrary l-state of the Hulthén potential with an improved approximation of the centrifugal term." Open Chemistry 9, no. 4 (2011): 737–42. http://dx.doi.org/10.2478/s11532-011-0050-6.

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AbstractAn approximate analytical solution of the radial Schrödinger equation for the generalized Hulthén potential is obtained by applying an improved approximation of the centrifugal term. The bound state energy eigenvalues and the normalized eigenfunctions are given in terms of hypergeometric polynomials. The results for arbitrary quantum numbers n r and l with different values of the screening parameter δ are compared with those obtained by the numerical method, asymptotic iteration, the Nikiforov-Uvarov method, the exact quantization rule, and variational methods. The results obtained by

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