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Journal articles on the topic 'Analytic solution'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Górecki, Henryk. "Analytic solution of transcendental equations." International Journal of Applied Mathematics and Computer Science 20, no. 4 (2010): 671–77. http://dx.doi.org/10.2478/v10006-010-0050-2.

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Analytic solution of transcendental equationsA decomposition technique of the solution of ann-th order linear differential equation into a set of solutions of 2-nd order linear differential equations is presented.

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2

Martynov, G. A. "Distribution functions of binary solutions (exact analytic solution)." Theoretical and Mathematical Physics 123, no. 3 (2000): 833–45. http://dx.doi.org/10.1007/bf02551037.

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3

Nazari, Mojtaba, Faisal Salah, Zainal Abdul Aziz, and Merbakhsh Nilashi. "Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/878349.

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The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM contains the auxiliary parameterħ, which provides us with a straightforward way to adjust and control the convergence region of the series solution. The resulted HAM solution at 8th-order and 14th-order approximation is then compared with that of the exact soliton solutions of KdV and Burgers equations,

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Abbasbandy, Saeid, Mahnaz Ashtiani, and Esmail Babolian. "Analytic Solution of the Sharma-Tasso-Olver Equation by Homotopy Analysis Method." Zeitschrift für Naturforschung A 65, no. 4 (2010): 285–90. http://dx.doi.org/10.1515/zna-2010-0404.

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An analytic technique, the homotopy analysis method (HAM), is applied to obtain the kink solution of the Sharma-Tasso-Olver equation. The homotopy analysis method is one of the analytic methods and provides us with a new way to obtain series solutions of such problems. HAM contains the auxiliary parameter ħwhich gives us a simple way to adjust and control the convergence region of series solution. “Due to this reason, it seems reasonable to rename ħthe convergence-control parameter” [1].

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LIAO, SHI-JUN. "A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate." Journal of Fluid Mechanics 385 (April 25, 1999): 101–28. http://dx.doi.org/10.1017/s0022112099004292.

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We apply a new kind of analytic technique, namely the homotopy analysis method (HAM), to give an explicit, totally analytic, uniformly valid solution of the two-dimensional laminar viscous flow over a semi-infinite flat plate governed by f‴(η)+αf(η)f″(η)+β[1−f′2(η)]=0 under the boundary conditions f(0)=f′(0)=0, f′(+∞)=1. This analytic solution is uniformly valid in the whole region 0[les ]η<+∞. For Blasius' (1908) flow (α=1/2, β=0), this solution converges to Howarth's (1938) numerical result and gives a purely analytic value f″(0)=0.332057. For the Falkner–Skan (1931) flow (α=1), it gives

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6

Abbasbandy, Saeid, Muhammet Yürüsoy, and Mehmet Pakdemirli. "The Analysis Approach of Boundary Layer Equations of Power-Law Fluids of Second Grade." Zeitschrift für Naturforschung A 63, no. 9 (2008): 564–70. http://dx.doi.org/10.1515/zna-2008-0906.

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A powerful analytic technique for nonlinear problems, the homotopy analysis method (HAM), is employed to give analytic solutions of power-law fluids of second grade. For the so-called secondorder power-law fluids, the explicit analytic solutions are given by recursive formulas with constant coefficients. Also, for the real power-law index in a quite large range an analytic approach is proposed. It is demonstrated that the approximate solution agrees well with the finite difference solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellen

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7

Wilkin, Francis P. "Modeling Nonaxisymmetric Bow Shocks: Solution Method and Exact Analytic Solutions." Astrophysical Journal 532, no. 1 (2000): 400–414. http://dx.doi.org/10.1086/308576.

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8

Cassell, J. S. "Analytic solution of algebraic equations." Annals of Nuclear Energy 28, no. 14 (2001): 1469–76. http://dx.doi.org/10.1016/s0306-4549(00)00131-6.

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9

Awawdeh, Fadi, Ahmad Adawi, and Safwan Al-Shara'. "Analytic Solution of Multipantograph Equation." Journal of Applied Mathematics and Decision Sciences 2008 (November 16, 2008): 1–10. http://dx.doi.org/10.1155/2008/605064.

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We apply the homotopy analysis method (HAM) for solving the multipantograph equation. The analytical results have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy analysis method. Comparisons are made to confirm the reliability of the homotopy analysis method.

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10

Xu, Liang, and Sha Xu. "Analytic Solution to a Virus Infection Model." Applied Mechanics and Materials 367 (August 2013): 503–7. http://dx.doi.org/10.4028/www.scientific.net/amm.367.503.

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A functional analytic method was developed by E.K.Ifantis in 1987 to prove that certain non-linear ordinary differential equations (ODEs) have a unique power series solution which converges absolutely in a specified disc of the complex plane. In this paper, we first applied this method to certain systems of two non-linear ordinary differential equations. We proved that the power series solutions can be determined by some recurrence relations which depend on the parameters of the equations and the initial conditions. Then, we found a method to extend the range of the converge bound. At last, we

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11

Remley, Kyle E., and David P. Griesheimer. "A SEMI-ANALYTIC EIGENVALUE EXTENSION TO THE DOPPLER SLAB ANALYTIC BENCHMARK1." EPJ Web of Conferences 247 (2021): 04018. http://dx.doi.org/10.1051/epjconf/202124704018.

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Advancement in multiphysics simulation has motivated interest in availability of analytic and semi-analytic benchmark solutions. These solutions are sought because they can be used to assess the accuracy of complicated numerical schemes necessary to simulate coupled physics systems. While there exist analytic solutions for fixed-source problems, benchmark-quality eigenvalue solutions are of interest because eigenvalue problems more closely align with analyses undertaken with coupled solvers. This paper extends a fixed-source benchmark, the Doppler Slab benchmark, to the eigenvalue case. A nove

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12

Bougoffa, Lazhar, Jun-Sheng Duan, and Randolph Rach. "Exact and approximate analytic solutions of the thin film flow of fourth-grade fluids by the modified Adomian decomposition method." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 8 (2016): 2432–40. http://dx.doi.org/10.1108/hff-07-2015-0278.

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Purpose The purpose of this paper is to first deduce a new form of the exact analytic solution of the well-known nonlinear second-order differential equation subject to a set of mixed nonlinear Robin and Neumann boundary conditions that model the thin film flows of fourth-grade fluids, and second to compare the approximate analytic solutions by the Adomian decomposition method (ADM) with the new exact analytic solution to validate its accuracy for parametric simulations of the thin film fluid flows, even for more complex models of non-Newtonian fluids in industrial applications. Design/methodo

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13

Cesarano, Clemente, Youssouf Massoun, Abderrezak Said, and Mohamed Elamine Talbi. "Analytic Study of Coupled Burgers’ Equation." Mathematics 11, no. 9 (2023): 2071. http://dx.doi.org/10.3390/math11092071.

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In this paper, we construct an analytical solution of the coupled Burgers’ equation, using the homotopy analysis method, which is a semi-analytical method, the approximate solution obtained by this method is convergent for different values of the convergence control parameter ℏ, the optimal value of ℏ corresponding with the minimum error to be determined by the residual. The results obtained by the present method are compared with other obtained solutions by different numerical methods.

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14

Zuhra, Samina, Noor Khan, Saeed Islam, and Rashid Nawaz. "Complexiton solutions for complex KdV equation by optimal Homotopy Asymptotic Method." Filomat 33, no. 19 (2019): 6195–211. http://dx.doi.org/10.2298/fil1919195z.

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In this article an innovative technique named as Optimal Homotopy Asymptotic Method has been explored to treat system of KdV equations computed from complex KdV equation. By developing special form of initial value problems to complex KdV equation, three different types of semi analytic complextion solutions fromcomplexKdVequation have been achieved. First semi analytic position solution received fromtrigonometric form of initial value problem, second is semi analytic negation solution received by hyperbolic form of initial value problem and third one is special type of semi analytic solution

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15

Ningsi, Gabariela Purnama, Fransiskus Nendi, and Lana Sugiarti. "An application of the finite difference method for solving the mass spring system equation." Jurnal Matematika, Statistika dan Komputasi 16, no. 3 (2020): 404. http://dx.doi.org/10.20956/jmsk.v16i3.9574.

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The numerical method is one method that can be used to solve differential equations, both differential equations that are easy or difficult to solve analytically. The solution obtained from the calculation results is an approximate solution or a solution that approaches an analytic solution, not an analytic solution. That is, in solving differential equations numerically, there is always an error. In this paper, an analytical solution is described and described and the application of different methods in solving a damped mass spring system with a known limit value. The error between the analyt

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16

Abdul Aziz, Zainal, Mojtaba Nazari, Faisal Salah, and Dennis Ling Chuan Ching. "Constant Accelerated Flow for a Third-Grade Fluid in a Porous Medium and a Rotating Frame with the Homotopy Analysis Method." Mathematical Problems in Engineering 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/601917.

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The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of a constant accelerated flow for a third-grade fluid in a porous medium and a rotating frame. HAM is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. The approximate analytic solution for constant accelerated flow is obtained by using HAM. HAM contains the auxiliary parameterℏ, which provides us with a straightforward way to obtain the convergence region of the series solution. Graphical results are plotted and the consequences discussed. The

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17

Segalman, Daniel J., Michael J. Starr, and Martin W. Heinstein. "New Approximations for Elastic Spheres Under an Oscillating Torsional Couple." Journal of Applied Mechanics 72, no. 5 (2004): 705–10. http://dx.doi.org/10.1115/1.1985430.

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The Lubkin solution for two spheres pressed together and then subjected to a monotonically increasing axial couple is examined numerically. The Deresiewicz asymptotic solution is compared to the full solution and its utility is evaluated. Alternative approximations for the Lubkin solution are suggested and compared. One approximation is a Padé rational function which matches the analytic solution over all rotations. The other is an exponential approximation that reproduces the asymptotic values of the analytic solution at infinitesimal and infinite rotations. Finally, finite element solutions

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18

Ghiasi, Emran Khoshrouye, and Reza Saleh. "Constructing analytic solutions on the Tricomi equation." Open Physics 16, no. 1 (2018): 143–48. http://dx.doi.org/10.1515/phys-2018-0022.

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AbstractIn this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To co

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19

Navnit, Jha, Perfilieva Irina, and Kritika. "High-resolution Fuzzy Component Scheme for Second-order Differential Equation Appearing in Single Commodity Stochastic Production Planning." Journal of Innovation Sciences and Sustainable Technologies 1, no. 3 (2021): 205–20. https://doi.org/10.0608/JISST.2022448367.

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The article deals with the second-order nonlinear differential equation that models stochastic production planning. We describe a fuzzy transform technique for obtaining the approximate analytic solution to a single commodity stochastic production-inventory model. In general, the classical solution is not known; thus, numerical treatment helps to analyze optimal inventory levels. The present description implements a fuzzy transform that approximates solutions at the interior of the domain with high-order accuracy. The approximate fuzzy components implementing a sinusoidal basic function are ar

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20

AL-Jawary, Majeed, and Sayl Abd- AL- Razaq. "Analytic and numerical solution for duffing equations." International Journal of Basic and Applied Sciences 5, no. 2 (2016): 115. http://dx.doi.org/10.14419/ijbas.v5i2.5838.

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<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components.

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21

Rezaee, Vahid, and Arash Houshmand. "NUMERICAL SOLUTION OF NON-SIMILAR BOUNDARY-LAYER FLOW OVER A CYLINDER." Journal of the Serbian Society for Computational Mechanics 17, no. 1 (2023): 134–50. http://dx.doi.org/10.24874/jsscm.2023.17.01.10.

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This paper presents Ð° numerical solution of a non-similar two-dimensional boundary-layer flow over a cylinder. The assumptions and related two-dimensional flow equations are presented. The fourth-order Runge-Kutta method with the backward differentiation formula (BDF) method to separation point is implemented in the numerical solution using MATLAB software. Numerical solution results are compared with well-known analytic solutions. Shear stress diagram, friction ratio based on Î¸ and x, and output results are illustrated. The results of numerical solution demonstrate good consistency with ana

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22

Bloor, M. I. G., and M. J. Wilson. "An approximate analytic solution method for the biharmonic problem." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2068 (2006): 1107–21. http://dx.doi.org/10.1098/rspa.2005.1603.

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A method is presented for the solution of the biharmonic equation through the use of a combination of polynomial and eigenfunction solutions. Results are presented comparing the method with an exact solution. Excellent agreement is obtained for economical solution representations. Calculations, and comparison with established results, of the displacement of an elastic plate under a uniform applied load are presented. Further, results are presented of the calculation of zero Reynolds number flow in a driven cavity.

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23

Bandura, Andriy. "Application of Hayman’s Theorem to Directional Differential Equations With Analytic Solutions in the Unit Ball." Studia Universitatis Babes-Bolyai Matematica 69, no. 2 (2024): 335–50. http://dx.doi.org/10.24193/subbmath.2024.2.06.

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In this paper, we investigate analytic solutions of higher order linear non-homogeneous directional differential equations whose coefficients are analytic functions in the unit ball. We use methods of theory of analytic functions in the unit ball having bounded L-index. Our proofs are based on application of inequalities from analog of Hayman’s theorem for analytic functions in the unit ball. There are presented growth estimates of their solutions which contain parameters depending on the coefficients of the equations. Also, we obtained sufficient conditions that every analytic solution of the

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24

Liu, Chein-Shan, Chung-Lun Kuo, and Chih-Wen Chang. "Decomposition–Linearization–Sequential Homotopy Methods for Nonlinear Differential/Integral Equations." Mathematics 12, no. 22 (2024): 3557. http://dx.doi.org/10.3390/math12223557.

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In the paper, two new analytic methods using the decomposition and linearization technique on nonlinear differential/integral equations are developed, namely, the decomposition–linearization–sequential method (DLSM) and the linearized homotopy perturbation method (LHPM). The DLSM is realized by an integrating factor and the integral of certain function obtained at the previous step for obtaining a sequential analytic solution of nonlinear differential equation, which provides quite accurate analytic solution. Some first- and second-order nonlinear differential equations display the fast conver

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25

Bradshaw-Hajek, Bronwyn H., and Philip Broadbridge. "Analytic solutions for calcium ion fertilisation waves on the surface of eggs – erratum." Mathematical Medicine and Biology: A Journal of the IMA 37, no. 3 (2020): 429–32. http://dx.doi.org/10.1093/imammb/dqaa002.

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Abstract The paper, “Analytic solutions for calcium ion fertilisation waves on the surface of eggs” by the current authors (this journal 2019), adopted an incorrect solution to Legendre’s equation that had been tabulated in a well known compendium of solutions of differential equations. The solution to the linear equation and the consequent solution of the considered nonlinear problem, are corrected here. The solution maintains the same character and the conclusions are the same. Numerical evaluations and graphic outputs have been modified.

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26

Kangro, Urve. "CORDIAL VOLTERRA INTEGRAL EQUATIONS AND SINGULAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN SPACES OF ANALYTIC FUNCTIONS∗." Mathematical Modelling and Analysis 22, no. 4 (2017): 548–67. http://dx.doi.org/10.3846/13926292.2017.1333970.

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We study general cordial Volterra integral equations of the second kind and certain singular fractional integro-differential equation in spaces of analytic functions. We characterize properties of the cordial Volterra integral operator in these spaces, including compactness and describe its spectrum. This enables us to obtain conditions under which these equations have a unique analytic solution. We also consider approximate solution of these equations and prove exponential convergence of approximate solutions to the exact solution.

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27

De Luca, Roberto, Marco Di Mauro, and Adele Naddeo. "Analytic solution of the lifeguard problem." Physics Education 53, no. 2 (2017): 023005. http://dx.doi.org/10.1088/1361-6552/aa9634.

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28

Eleuch, H., Y. V. Rostovtsev, and M. O. Scully. "New analytic solution of Schrödinger's equation." EPL (Europhysics Letters) 89, no. 5 (2010): 50004. http://dx.doi.org/10.1209/0295-5075/89/50004.

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29

Jin-Feng, Liao, and Zhuang Peng-Fei. "Analytic Solution of Strongly Coupling SchrödingerEquations." Communications in Theoretical Physics 41, no. 4 (2004): 502–8. http://dx.doi.org/10.1088/0253-6102/41/4/502.

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30

Frumin, Leonid L., Gleb V. Zilberstein, and Sergey E. Peltek. "The isoelectric focusing problem analytic solution." Journal of Biochemical and Biophysical Methods 45, no. 2 (2000): 205–9. http://dx.doi.org/10.1016/s0165-022x(00)00118-4.

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31

Sengül, Metin. "Analytic solution of the Feldtkeller equation." AEU - International Journal of Electronics and Communications 63, no. 8 (2009): 632–37. http://dx.doi.org/10.1016/j.aeue.2008.05.003.

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32

Wang, Chui-Lin. "An analytic solution of C60molecular orbitals." Journal of Physics: Condensed Matter 5, no. 32 (1993): 5851–58. http://dx.doi.org/10.1088/0953-8984/5/32/014.

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33

Hodges, Hardy M. "Analytic solution of a chaotic inflaton." Physical Review D 39, no. 12 (1989): 3568–70. http://dx.doi.org/10.1103/physrevd.39.3568.

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34

Yang, Yaguang, та Zhiqiang Zhou. "An analytic solution to Wahbaʼs problem". Aerospace Science and Technology 30, № 1 (2013): 46–49. http://dx.doi.org/10.1016/j.ast.2013.07.002.

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35

Thornber, K. K., and L. R. Williams. "Analytic solution of stochastic completion fields." Biological Cybernetics 75, no. 2 (1996): 141–51. http://dx.doi.org/10.1007/s004220050282.

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36

Kufner, Tobias, Günter Leugering, Johannes Semmler, Michael Sting, and Christoph Strohmeyer. "Simulation and structural optimization of 3d Timoshenko beam networks based on fully analytic network solutions." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 6 (2018): 2409–31. http://dx.doi.org/10.1051/m2an/2018065.

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This article is concerned with the efficient and accurate simulation and optimization of linear Timoshenko beam networks subjected to external loads. A solution scheme based on analytic ansatz-functions known to provide analytic solutions for the deformation and rotation of a single beam with given boundary data is extended to the full network. It is demonstrated that the analytic approach is equivalent to a finite element (FE) method where only one element with a suitably chosen shape function per beam is required. The solution of the FE-type system provides analytic solutions at the nodes, f

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37

Zheng, Kun, Yu Miao, Tong Li, et al. "Anti-function solution of uniaxial anisotropic Stoner–Wohlfarth model." Chinese Physics B 31, no. 4 (2022): 040202. http://dx.doi.org/10.1088/1674-1056/ac401e.

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The anti-trigonometric function is used to strictly solve the uniaxial anisotropic Stoner–Wohlfarth (SW) model, which can obtain the relation of the angle α(θ) between the magnetization (the anisotropy field) and the applied magnetic field. Using this analytic solution, the hysteresis loops of uniaxial anisotropic SW particles magnetized in typical directions could be numerically calculated. Then, the hysteresis loops are obtained in randomly distributed SW particle ensembles while ignoring the dipole interaction among them with the analytic solution. Finally, the correctness of the analytic s

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38

Kuksin, Sergei, and Nikolai Nadirashvili. "Analyticity of solutions for quasilinear wave equations and other quasilinear systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 6 (2014): 1155–69. http://dx.doi.org/10.1017/s0308210512001801.

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We prove the persistence of analyticity for classical solutions of the Cauchy problem for quasilinear wave equations with analytic data. Our results show that the analyticity of solutions, stated by the Cauchy–Kowalewski and Ovsiannikov–Nirenberg theorems, lasts until a classical solution exists. Moreover, they show that if the equation and the Cauchy data are analytic only in a part of the space variables, then a classical solution is also analytic in these variables. The approach applies to other quasilinear equations and implies the persistence of the space analyticity (and the partial spac

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Bradshaw-Hajek, Bronwyn H., and Philip Broadbridge. "Analytic solutions for calcium ion fertilisation waves on the surface of eggs." Mathematical Medicine and Biology: A Journal of the IMA 36, no. 4 (2019): 549–62. http://dx.doi.org/10.1093/imammb/dqz002.

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Abstract The evolution of calcium fertilisation waves on the cortex of amphibian eggs can be described by a nonlinear reaction-diffusion process on the surface of a sphere. Here, we use the nonclassical symmetry technique to find an exact analytic solution that describes the evolution of the calcium concentration. The solutions presented compare well with published experimental results. The analytic solution can be used to give insight into the processes governing the fertilisation wave, such as the flow of calcium ions from the sperm entry point. By finding a spiral solution to an approximate

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40

Yokus, Asıf, Hülya Durur, Hijaz Ahmad, and Shao-Wen Yao. "Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation." Mathematics 8, no. 6 (2020): 908. http://dx.doi.org/10.3390/math8060908.

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In this paper, a new solution process of ( 1 / G ′ ) -expansion and ( G ′ / G , 1 / G ) -expansion methods has been proposed for the analytic solution of the Zhiber-Shabat (Z-S) equation. Rather than the classical ( G ′ / G , 1 / G ) -expansion method, a solution function in different formats has been produced with the help of the proposed process. New complex rational, hyperbolic, rational and trigonometric types solutions of the Z-S equation have been constructed. By giving arbitrary values to the constants in the obtained solutions, it can help to add physical meaning to the traveling wave

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41

Liu, Chein-Shan, Botong Li, and Chung-Lun Kuo. "Variational Iteration and Linearized Liapunov Methods for Seeking the Analytic Solutions of Nonlinear Boundary Value Problems." Mathematics 13, no. 3 (2025): 354. https://doi.org/10.3390/math13030354.

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The boundary shape function method (BSFM) and the variational iteration method (VIM) are merged together to seek the analytic solutions of nonlinear boundary value problems. The boundary shape function method transforms the boundary value problem to an initial value problem (IVP) for a new variable. Then, a modified variational iteration method (MVIM) is created by applying the VIM to the resultant IVP, which can achieve a good approximate solution to automatically satisfy the prescribed mixed-boundary conditions. By using the Picard iteration method, the existence of a solution is proven with

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42

Ðordjevic, Jasmina. "Some analytic approximations for backward stochastic differential equations." Filomat 34, no. 7 (2020): 2235–51. http://dx.doi.org/10.2298/fil2007235d.

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We consider an analytic iterative method to approximate the solution of the backward stochastic differential equation of general type. More precisely, we define a sequence of approximate equations and give sufficient conditions under which the approximate solutions converge with probability one and in pth moment sense, p ? 2, to the solution of the initial equation under Lipschitz condition. The Z-algorithm for this iterative method is introduced and some examples are presented to illustrate the theory.

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43

Goldstein-Tweg, Tom, Elinor Ginzburg-Ganz, Juri Belikov, and Yoash Levron. "Uniqueness of Optimal Power Management Strategies for Energy Storage Dynamic Models." Energies 18, no. 6 (2025): 1483. https://doi.org/10.3390/en18061483.

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This paper contributes to the field of analytic and semi-analytic solutions for optimal power flow problems involving storage systems. Its primary contribution is a rigorous proof establishing the uniqueness of the “shortest path” optimal solution, a key element in this class of algorithms, building upon a graphical design procedure previously introduced. The proof is constructed through five consequential lemmas, each defining a distinct characteristic of the optimal solution. These characteristics are then synthesized to demonstrate the uniqueness of the optimal solution, which corresponds t

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44

Kim, Jeongin, and Yong Sung Park. "ANALYTIC SOLUTION FOR THE VELOCITY FIELD AROUND SUBMERGED PERMEABLE BREAKWATERS." Coastal Engineering Proceedings, no. 37 (September 1, 2023): 15. http://dx.doi.org/10.9753/icce.v37.structures.15.

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In this paper, an analytic solution to the scattering of water wave by submerged permeable breakwaters in infinite-depth water is presented. The analytic solution of the velocity field around the permeable breakwater under the linear wave train in deep water condition is sought by formulating a nonhomogeneous Riemann-Hilbert problem. To deal with the nonlinearity due to the permeability of the plates, a perturbation method is applied in terms of a small parameter representing permeability. We present the leading order solution (impermeable breakwaters) and the first order solution (permeable b

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Asghar, S., S. Nadeem, K. Hanif, and T. Hayat. "Analytic solution of Stokes second problem for second-grade fluid." Mathematical Problems in Engineering 2006 (2006): 1–8. http://dx.doi.org/10.1155/mpe/2006/72468.

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Using Laplace transformation and perturbation techniques, analytical solution is obtained for unsteady Stokes' second problem. Expressions for steady and transient solutions are explicitly determined. These solutions depend strongly upon the material parameter of second-grade fluid. It is shown that phase velocity decreases by increasing material parameter of second-grade fluid.

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Perry, R. L., J. D. Massie, and P. T. Cummings. "An analytic model for aqueous electrolyte solutions based on fluctuation solution theory." Fluid Phase Equilibria 39, no. 3 (1988): 227–66. http://dx.doi.org/10.1016/0378-3812(88)85007-6.

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Liu, Ling Xia. "Analytic Solutions of an Iterative Functional Differential Equation." Key Engineering Materials 474-476 (April 2011): 2208–12. http://dx.doi.org/10.4028/www.scientific.net/kem.474-476.2208.

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This paper is concerned with the existence of analytic solutions of an iterative functional differential equation. By constructing a convergent power series solution of an auxiliary equation, analytic solutions for the original differential equation are obtained. We discuss not only those α at the hyperbolic case 0<|α|<1 but also those α near resonance under Diophantine condition.

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Nagai, Baku M., Muhammed Sohel Rana, and Kazumasa Ameku. "C11 Simple Analytic Solution for Flow around an Abruptly Appeared Vortex Filament." Proceedings of Conference of Kyushu Branch 2007.60 (2007): 77–78. http://dx.doi.org/10.1299/jsmekyushu.2007.60.77.

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Lehmann, Moritz, and Stephan Gekle. "Analytic Solution to the Piecewise Linear Interface Construction Problem and Its Application in Curvature Calculation for Volume-of-Fluid Simulation Codes." Computation 10, no. 2 (2022): 21. http://dx.doi.org/10.3390/computation10020021.

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The plane–cube intersection problem has been discussed in the literature since 1984 and iterative solutions to it have been used as part of piecewise linear interface construction (PLIC) in computational fluid dynamics simulation codes ever since. In many cases, PLIC is the bottleneck of these simulations regarding computing time, so a faster analytic solution to the plane–cube intersection would greatly reduce the computing time for such simulations. We derive an analytic solution for all intersection cases and compare it to the previous solution from Scardovelli and Zaleski (Scardovelli, R.;

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Malysheva, L. I. "Analytic Analysis of Electronic and Transport Properties of Finite Polyenes." Ukrainian Journal of Physics 66, no. 7 (2021): 619. http://dx.doi.org/10.15407/ujpe66.7.619.

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Various important characteristics of finite polyene chains are found on the basis of approximate solutions of the characteristic equations. The obtained approximate and limit expressions for the wave functions, energy gap, etc. can be used for the analysis of the electronic and transport properties of polyenes, which gives a deeper understanding of the fundamental properties of finite alternating polyene chains. We also demonstrate the high efficiency of the proposed approximations as a zero-order estimate for the numerical solution of the characteristic equation.

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