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Journal articles on the topic 'Analytical-numerical method'

Author: Grafiati

Published: 28 May 2022

Last updated: 25 July 2025

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1

Коrniyenko, Yu V., and M. G. Suryaninov. "Development of CAD implementing the algorithm of boundary elements’ numerical analytical method." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 1 (March 31, 2015): 128–33. http://dx.doi.org/10.15276/opu.1.45.2015.21.

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2

Krutii, Yu, V. Osadchiy, and V. Surianinov. "CALCULATION OF A CULVER PIPE BY THE NUMERICAL-ANALYTICAL BOUNDARY ELEMENTS METHOD." Mechanics And Mathematical Methods 7, no. 1 (2025): 15–25. https://doi.org/10.31650/2618-0650-2025-7-1-15-25.

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The methodology for applying the numerical-analytical boundary elements method to the calculation of reinforced concrete and fiber-reinforced concrete culverts is considered. The force state of the pipe as part of the road embankment from the action of the soil mass and moving vehicle load is determined by an alternating diagram of bending moments with a maximum positive moment in the ridge and trough sections and a maximum negative moment in the side sections, which necessitates the need for double rod reinforcement. Such reinforcement has low efficiency. It is difficult to ensure the design

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3

Bezrodnykh, S. I., and S. V. Pikulin. "Numerical-analytical method for the Burgers equation." Contemporary Mathematics. Fundamental Directions 69, no. 2 (2023): 208–23. http://dx.doi.org/10.22363/2413-3639-2023-69-2-208-223.

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We construct an efficient numerical-analytical method for solving the initial-boundary value problem for the Burgers equation on a segment with a periodic boundary condition. The method includes the reduction to a linear problem based on an explicit-implicit time discretization scheme and an analytical solution of an auxiliary linear problem at each time step using the explicit form of the corresponding Green’s function. The efficiency of the constructed method is due to the fact that the algorithm for solving the auxiliary problem has only linear complexity in terms of the number of spatial d

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4

Kolchunov, Vladimir I. "Numerical-analytical method in reinforced concrete mechanics." Structural Mechanics of Engineering Constructions and Buildings 18, no. 6 (2022): 525–33. http://dx.doi.org/10.22363/1815-5235-2022-18-6-525-533.

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A variant of the numerical-analytical method in the nonlinear mechanics of reinforced concrete is proposed. Calculation models make it possible to take into account a number of important factors, such as discrete cracks, the effect of concrete discontinuity, and reinforcement reactions in a crack. When solving the inverse problem of determining the width of the crack opening, the deformation effect is not set, but is modeled using the “joining” of the assigned minimum possible width, its opening under the appropriate loading. In the calculation scheme, pairs of finite elements are distinguishe

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Afradi, Alireza, Iraj Alavi, and Mahdieh Moslemi. "Selecting the best mining method using analytical and numerical methods." Journal of Sedimentary Environments 6, no. 3 (2021): 403–15. http://dx.doi.org/10.1007/s43217-021-00063-6.

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6

Lazareva, D. V., and M. G. Suryaninov. "Mathematical model of complex technical asymmetric system based on numerical-analytical boundary elements method." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 2 (June 15, 2015): 133–37. http://dx.doi.org/10.15276/opu.2.46.2015.24.

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7

Epstein, Ronald J., and Donald B. Bliss. "Aeroacoustic Boundary Element Method Using Analytical/Numerical Matching." AIAA Journal 35, no. 2 (1997): 244–54. http://dx.doi.org/10.2514/2.114.

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8

Epstein, Ronald J., and Donald B. Bliss. "Aeroacoustic boundary element method using analytical/numerical matching." AIAA Journal 35 (January 1997): 244–54. http://dx.doi.org/10.2514/3.13494.

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9

Akulenko, L. D., S. A. Kumakshev, and S. V. Nesterov. "A numerical-analytical method for investigating parametric oscillations." Journal of Applied Mathematics and Mechanics 79, no. 2 (2015): 111–21. http://dx.doi.org/10.1016/j.jappmathmech.2015.07.001.

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10

Berzan, Vladimir. "COMPARATIVE ANALYSIS OF METHODS OF CALCULATION IN TRANSIENT AND WAVE PROCESSES IN ELECTRIC CIRCUITS." Journal of Engineering Science XXVI (2) (June 18, 2019): 40–57. https://doi.org/10.5281/zenodo.3249182.

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The problem of calculating the transient and wave processes in the circuits with the concentrated and distributed parameters is examined. A comparative-qualitative analysis of the analytical and numerical methods used for these purposes was carried out, indicating the advantages and disadvantages of their application. It is presented algorithms for applying the examined methods. It is found that numerical calculation methods have many advantages in studying stationary and dynamic processes in the natural sequence of processes course in the circuit. It is recommended to use the finite differenc

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11

Vakulenko, Aleksei M., and Alexander S. Bolshev. "Loads from Ice Ridge Keels – Analytical vs. Numerical." Applied Mechanics and Materials 725-726 (January 2015): 229–34. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.229.

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Action of ice ridge keel on vertical structures is studied by means of analytical and numerical methods. The analytical method involves keel load calculations using Russian and European recommendations provided in SP 38.13330.2012 and ISO/FDIS 19906 respectively. The numerical method involves finite element calculation. It is demonstrated that numerical methods can provide an important insight into ridges keels behavior. The numerical and analytical results obtained using Russian recommendations for vertical structures are in a good agreement.

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12

Panou, G., and R. Korakitis. "Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates." Journal of Geodetic Science 11, no. 1 (2021): 111–21. http://dx.doi.org/10.1515/jogs-2020-0126.

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Abstract In this work, two analytical and two numerical methods of converting Cartesian to ellipsoidal coordinates of a point in space are presented. After slightly modifying a well-known exact analytical method, a new exact analytical method is developed. Also, two well-known numerical methods, which were developed for points exactly on the surface of a triaxial ellipsoid, are generalized for points in space. The four methods are validated with numerical experiments using an extensive set of points for the case of the Earth. Then, a theoretical and a numerical comparative assessment of the fo

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13

Romão, E. C., M. D. De Campos, and L. F. M. De Moura. "GALERKIN FINITE ELEMENT METHOD AND FINITE DIFFERENCE METHOD FOR SOLVING CONVECTIVE NON-LINEAR EQUATION." Revista de Engenharia Térmica 9, no. 1-2 (2010): 69. http://dx.doi.org/10.5380/reterm.v9i1-2.61935.

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The fast progress has been observed in the development of numerical and analytical techniques for solving convection-diffusion and fluid mechanics problems. Here, a numerical approach, based in Galerkin Finite Element Method with Finite Difference Method is presented for the solution of a class of non-linear transient convection-diffusion problems. Using the analytical solutions and the L2 and L∞ error norms, some applications is carried and valuated with the literature.

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14

LUKIANOV, Petro. "NUMERICAL-ANALYTICAL METHOD FOR THE PROBLEMS OF ENVIROMENTAL SAFETY." CHERKASY UNIVERSITY BULLETIN: APPLIED MATHEMATICS. INFORMATICS, no. 1 (2022): 13–22. http://dx.doi.org/10.31651/2076-5886-2021-1-13-22.

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15

Epstein, Ronald J., and Donald B. Bliss. "An acoustic boundary element method using analytical/numerical matching." Journal of the Acoustical Society of America 101, no. 1 (1997): 92–106. http://dx.doi.org/10.1121/1.417969.

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16

Pikulin, S. V. "Analytical-Numerical Method for Calculating the Thomas-Fermi Potential." Russian Journal of Mathematical Physics 26, no. 4 (2019): 544–52. http://dx.doi.org/10.1134/s1061920819040113.

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17

Arafa, A. R. A. "Analytical numerical method for solving nonlinear partial differential equations." Applied Mathematics Letters 9, no. 4 (1996): 115–22. http://dx.doi.org/10.1016/0893-9659(96)00062-6.

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18

Chuanxia, Rao. "AN ANALYTICAL–NUMERICAL METHOD FOR A TYPICAL BIFURCATION PROBLEM." Acta Mathematica Scientia 7, no. 3 (1987): 241–46. http://dx.doi.org/10.1016/s0252-9602(18)30449-1.

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19

Fiqih, Achmad Zul, Juswan, and Muhammad Zubair Muis Alie. "Beam deflection analysis using the analytical and numerical method." IOP Conference Series: Earth and Environmental Science 575 (October 29, 2020): 012196. http://dx.doi.org/10.1088/1755-1315/575/1/012196.

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20

CHEVILLOTTE, Fabien. "Porous material characterization with Bayesian and machine learning method." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 270, no. 2 (2024): 9590–97. http://dx.doi.org/10.3397/in_2024_4269.

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Two main classes of characterization methods are usually employed for acoustic parameters of porous media, namely the analytical inversion method or the numerical fitting procedure. While analytical inverse methods suffer from a high sensivity to the operator, the numerical fitting methods can lead to non physical sets of parameters. The fitting procedure can be bounded by the analytical inversion. The Bayesian method, which is presented in this work, is the appropriate tool to couple these methods. It enables to carry out a numerical fitting procedure using the analytical inversion as prior e

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21

Sudi, Mungkasi, and Widjaja Damar. "A numerical-analytical iterative method for solving an electrical oscillator equation." TELKOMNIKA (Telecommunication, Computing, Electronics and Control) 19, no. 4 (2021): 1218–25. https://doi.org/10.12928/telkomnika.v19i4.18987.

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Self-excited oscillation problem occurring from a triode electrical circuit has been modelled by van der Pol. Until now, the exact solution to the van der Pol equation is not available. This paper focuses on finding a new method for solving the van der Pol equation simply and accurately. There exists several approximate iterative methods available in the literature for solving the van der Pol equation, such as, the successive approximation method. The successive approximation method is simple, but inaccurate for large time values. In this paper, we propose a new variant of numerical-analytical

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22

Devia Narváez, Diana Marcela, Fernando Mesa, and German Correa-Vélez. "Numerical comparison by different methods (second order Runge Kutta methods, Heun method, fixed point method and Ralston method) to differential equations with initial condition." Scientia et Technica 25, no. 2 (2020): 299–305. http://dx.doi.org/10.22517/23447214.24446.

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This manuscript contains a detailed comparison between numerical solution methods of ordinary differential equations, which start from the Taylor series method of order 2, stating that this series hinders calculations for higher order derivatives of functions of several variables, so that the Runge Kutta methods of order 2 are implemented, which achieve the required purpose avoiding the cumbersome calculations of higher order derivatives. In this document, different variants of the Runge-Kutta methods of order 2 will be exposed from an introduction and demonstration of the connection of these

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23

Opanuga, A. A., S. O. Edeki, H. I. Okagbue, G. O. Akinlabi, A. S. Osheku, and B. Ajayi. "On numerical solutions of systems of ordinary differential equations by numerical-analytical method." Applied Mathematical Sciences 8 (2014): 8199–207. http://dx.doi.org/10.12988/ams.2014.410807.

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24

Lukianov, Petro. "Numerical–analitical method for the problems of aerodynamic noise generations in helicopter and quadrotors." Aerospace Technic and Technology, no. 6 (November 21, 2024): 34–46. https://doi.org/10.32620/aktt.2024.6.03.

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The subject of this paper is to demonstrate the capabilities of numerical-analytical method for solving problems of sound generation by helicopter and quadrocopter rotors. In particular, the finite difference schemes for the implementation of the numerical-analytical method for steady, non-steady 2-D potential flows describing the generation of noise of aerodynamic origin by a helicopter rotor blade are presented. Examples of the application of the numerical-analytical method to the problems of sound generation by a 3-D unsteady potential flow for the aerodynamic noise of a quadrotor are prese

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25

Olsen, Anders Lau, and Henrik Gordon Petersen. "Inverse kinematics by numerical and analytical cyclic coordinate descent." Robotica 29, no. 4 (2010): 619–26. http://dx.doi.org/10.1017/s026357471000038x.

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SUMMARYCyclic coordinate descent (CCD) inverse kinematics methods are traditionally derived only for manipulators with revolute and prismatic joints. We propose a new numerical CCD method for any differentiable type of joint and demonstrate its use for serial-chain manipulators with coupled joints. At the same time more general and simpler to derive, the method performs as well in experiments as the existing analytical CCD methods and is more robust with respect to parameter settings. Moreover, the numerical method can be applied to a wider range of cost functions.

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26

ÜNAL, Osman, and Nuri AKKAŞ. "An Innovative Approach for Numerical Solution of the Unsteady Convection-Dominated Flow Problems." Karadeniz Fen Bilimleri Dergisi 12, no. 2 (2022): 1069–80. http://dx.doi.org/10.31466/kfbd.1165640.

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In this study, convection-diffusion equation is solved numerically using four different space discretization methods namely first-order upwinding, second-order central difference, cubic (partially upwinded) and cubic-TVD (Total Variation Diminishing) techniques. All methods are compared with the analytical solution. The first-order method is not close to the analytical solution due to the numerical dispersion. The higher-order techniques reduce numerical dispersion. However, they cause another numerical error, unphysical oscillation. This study proposes an innovative approach on cubic-TVD meth

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27

Han, Chaoshuai, Yongliang Ma, Xianqiang Qu, and Mindong Yang. "An Analytical Solution for Predicting the Vibration-Fatigue-Life in Bimodal Random Processes." Shock and Vibration 2017 (2017): 1–18. http://dx.doi.org/10.1155/2017/1010726.

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Predicting the vibration-fatigue-life of engineering structures subjected to random loading is a critical issue for. Frequency methods are generally adopted to deal with this problem. This paper focuses on bimodal spectra methods, including Jiao-Moan method, Fu-Cebon method, and Modified Fu-Cebon method. It has been proven that these three methods can give acceptable fatigue damage results. However, these three bimodal methods do not have analytical solutions. Jiao-Moan method uses an approximate solution, Fu-Cebon method, and Modified Fu-Cebon method needed to be calculated by numerical integ

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28

Maulana, Z. S., M. F. R. Rizaldi, and M. A. Bustomi. "The Results Comparison of Numerical and Analytical Methods for Electric Potential on Rectangular Pipes." Journal of Physics: Conference Series 2623, no. 1 (2023): 012036. http://dx.doi.org/10.1088/1742-6596/2623/1/012036.

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Abstract Two methods can be used to solve the problem of electric potential distribution in a rectangular pipe: numerical and analytical. The analytical solution is obtained using the Laplace equation and the given boundary conditions to complete the solution in the form of a linear combination of sinusoidal and hyperbolic functions. While the numerical solution is obtained using the finite difference method in the Python programming language. The comparison between the analytical and numerical solutions shows that the two have a good fit. This can be seen from the graph of the electric potent

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29

Abdukhamidov, Sardor, and Lobar Chorshanbiyeva. "SOLVING RESEARCH PROBLEMS OF FLOWS IN CHANNELS USING NUMERICAL METHODS." TECHNICAL SCIENCE RESEARCH IN UZBEKISTAN 2, no. 6 (2024): 142–45. https://doi.org/10.5281/zenodo.12548425.

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The study of fluid flow in channels is fundamental in various fields of engineering and environmental sciences. Traditional analytical methods often fall short in handling complex geometries and varying boundary conditions. Numerical methods have thus become indispensable in understanding and predicting fluid dynamics in channels. This paper explores the application of numerical methods in the study of flows in channels, focusing on the Finite Difference Method (FDM), Finite Element Method (FEM), and Computational Fluid Dynamics (CFD). Case studies and simulations are presented to illustrate t

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30

Sivandzade, Farzane. "AN ANALYTICAL MODEL FOR PREDICTION OF CONTROLLED RELEASE FROM BULK BIODEGRADING POLYMER MICROSPHERES." Asian Journal of Pharmaceutical and Clinical Research 11, no. 3 (2018): 432. http://dx.doi.org/10.22159/ajpcr.2018.v11i3.23219.

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Objective: A convenient numerical model has been developed to predict release profile of different types of agents from bulk biodegrading polymer microspheres, including magnitude methods are less accurate than analytical methods. Usually, this study used analytical solutions for the model and compared the analytical results with numerical solution and experimental data.Methods: The objective drug controlled release profiles were modeled based on a four-phase pattern. Then, a specific formulation was considered based on Fick’s second law. After calculating various parameters, the equations wer

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31

Faria, Geovanne Silva, Andreia Aoyagui Nascimento, and Felipe Pamplona Mariano. "Comparison of the combinations of Fourier pseudospectral method, finite volume method, Euler method and fourth order Runge-Kutta method used to solve Burgers equation." Cuadernos de Educación y Desarrollo 16, no. 13 (2024): e6975. https://doi.org/10.55905/cuadv16n13-100.

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The Burgers equation is a mathematical model frequently used in Computational Fluid Dynamics. It is often employed to test and calibrate numerical methods, as it is one of the few nonlinear transport equations with an exact analytical solution. In this paper, numerical solutions are obtained using the Finite Difference Method (FDM) and the Fourier Pseudospectral Method (FPSM) for spatial discretization, combined with the Euler Method and the Fourth-Order Runge-Kutta Method (FRKM) for time discretization. The results are compared with the exact analytical solution in terms of accuracy, converge

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32

Abdel-Aty, M. A., and M. A. Abdou. "Analytical and numerical discussion for the quadratic integral equations." Filomat 37, no. 24 (2023): 8095–111. http://dx.doi.org/10.2298/fil2324095a.

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In this work, we study the existence of at least one solution of the Quadratic integral equation with Phase-lag term. Our proof depends on a suitable combination of the Darbo?s fixed point principle and the technique of measures of noncompactness. Homotopy perturbation method is presented to obtain an approximate solution of Quadratic integral equation with Phase-lag term. Convergence and error estimate of Homotopy perturbation method are obtained. Homotopy perturbation method is a powerful device for solving a wide variety of problems. It gives excellent flexibility to the expression of the s

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33

Nave, OPhir. "Modification of Semi-Analytical Method Applied System of ODE." Modern Applied Science 14, no. 6 (2020): 75. http://dx.doi.org/10.5539/mas.v14n6p75.

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In this study, we modify the well-known semi-analytical method called the Homotopy Analysis Method (HAM), such that the right-hand side of a given ODE system is decomposed to a sum of analytical functions. We called the new semi-analytical method: decomposition of the Homotopy Analysis Method (DHAM). We applied the new method to a breast cancer mathematical model. We compared the DHAM results to HAM and numerical simulations. We concluded that the DHAM results are closer to the numerical simulation results than the HAM.

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34

Moore, Travis J., and Vedat S. Ertürk. "Comparison of the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems in engineering." Nonlinear Engineering 9, no. 1 (2019): 1–13. http://dx.doi.org/10.1515/nleng-2018-0148.

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AbstractSolutions to nonlinear boundary value problems modelling physical phenomena in engineering applications have traditionally been approximated using numerical methods. More recently, several semi-analytical methods have been developed and used extensively in diverse engineering applications. This work compares the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems arising in engineering. The accuracy and efficiency of the method of variation of parameters are compared to those of two widely used semi-analytical methods, the Adomian

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35

Rakisheva, D. S., Igor N. Modin, and B. G. Mukanova. "Mapes of secondary sources in the problem of ERT probing 2D medium: numerical method and analytical solutions." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 98, no. 2 (2020): 204–13. http://dx.doi.org/10.31489/2020m2/204-213.

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36

Masėnas, Juozas, Remigijus Šalna, Linas Juknevičius, and Juozas Valivonis. "Analytical Method and Analysis of Cold-Joint Interface." Applied Sciences 13, no. 7 (2023): 4176. http://dx.doi.org/10.3390/app13074176.

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The behaviour of the interface between two concrete layers, subjected to shear, is a complex process that is influenced by many different parameters. Knowledge of concrete interface performance is insufficient to this day. Most of the existing analytical methods are only suitable for determining the highest interface shear resistance and do not consider the interface behaviour at other stages. This article focuses on smooth concrete interfaces, which have their layers cast at different times (cold-joint interface). By analysing the results of different experimental push-off tests, presented in

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37

Liu, Yue, Noam Weisbrod, and Alexander Yakirevich. "Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer." Water 11, no. 6 (2019): 1168. http://dx.doi.org/10.3390/w11061168.

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Various delineation methods, ranging from simple analytical solutions to complex numerical models, have been applied for wellhead protection area (WHPA) delineation. Numerical modeling is usually regarded as the most reliable method, but the uncertainty of input parameters has always been an obstacle. This study aims at examining the results from different WHPA delineation methods and addressing the delineation uncertainty of numerical modeling due to the uncertainty from input parameters. A comparison and uncertainty analysis were performed at two pumping sites—a single well and a wellfield c

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38

Alexeev, G. A., A. P. Kusaykin, and A. Ye Poyedinchuk. "An Analytical Numerical Method for Solution of Refraction Inverse Problem." Telecommunications and Radio Engineering 53, no. 11 (1999): 1–11. http://dx.doi.org/10.1615/telecomradeng.v53.i11.10.

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39

Kuznetsov, N. V., G. A. Leonov, and V. I. Vagaitsev. "Analytical-numerical method for attractor localization of generalized Chua's system*." IFAC Proceedings Volumes 43, no. 11 (2010): 29–33. http://dx.doi.org/10.3182/20100826-3-tr-4016.00009.

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40

Cherepennikov, V. B. "Numerical analytical method of studying some linear functional differential equations." Numerical Analysis and Applications 6, no. 3 (2013): 236–46. http://dx.doi.org/10.1134/s1995423913030075.

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41

Sochilin, A. V., and S. I. Eminov. "A numerical–analytical method for calculation of curved dipole antennas." Journal of Communications Technology and Electronics 62, no. 1 (2017): 55–60. http://dx.doi.org/10.1134/s1064226917010132.

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Song, Y. C., J. Ding, and C. J. Guo. "A semi-analytical numerical method for fast metamaterial absorber design." AIP Advances 5, no. 9 (2015): 097108. http://dx.doi.org/10.1063/1.4930531.

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Das-Gupta, D. K., and J. S. Hornsby. "Laser-intensity modulation method (LIMM)-an analytical and numerical modification." IEEE Transactions on Electrical Insulation 26, no. 1 (1991): 63–68. http://dx.doi.org/10.1109/14.68229.

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44

Shevchenko, V. P., and R. N. Neskorodev. "A Numerical–Analytical Method for Solving Problems of Linear Viscoelasticity." International Applied Mechanics 50, no. 3 (2014): 263–73. http://dx.doi.org/10.1007/s10778-014-0629-7.

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45

LAUKO, M., and D. ŠEVČOVIČ. "COMPARISON OF NUMERICAL AND ANALYTICAL APPROXIMATIONS OF THE EARLY EXERCISE BOUNDARY OF AMERICAN PUT OPTIONS." ANZIAM Journal 51, no. 4 (2010): 430–48. http://dx.doi.org/10.1017/s1446181110000854.

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AbstractWe present qualitative and quantitative comparisons of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of American put options paying zero dividends. We analyse the asymptotic behaviour of these methods close to expiration, and introduce a new numerical scheme for computing the early exercise boundary. Our local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over-relaxation method and the analy

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46

Kozelskaya, Maria, Daria Donskova, Vera Ulianskaya, and Pavel Shvetsov. "Stress strain behavior research of triangular dam using analytical and numerical methods." MATEC Web of Conferences 251 (2018): 04043. http://dx.doi.org/10.1051/matecconf/201825104043.

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The article deals with the calculation of triangular dams by numerical and analytical methods. The analytical solution is performed by a semi-inverse method. The stress function is taken as a polynomial of the third degree. Numerical calculation is performed using the finite element method. A comparison of the results obtained by the two methods is performed.

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47

Koffi J. AGBELELE, Ernesto C. HOUEHANOU, Marx Ferdinand AHLINHAN, Abdoul W. ALI, and Houngan Comlan Aristide. "Assessment of Slope Stability by the Fellenius Slice Method: Analytical and numerical approach." World Journal of Advanced Research and Reviews 18, no. 2 (2023): 1205–14. http://dx.doi.org/10.30574/wjarr.2023.18.2.0874.

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Slope stability is a topic of great importance in civil engineering, as slope failures can cause considerable damage to infrastructure and downstream properties. In this study, we applied the Fellenius slice method, using both the analytical method, as well as the numerical method, which was performed using the SLOPE/W module of the Geostudio software. The results obtained by both methods showed that the increase in soil cohesion improves the stability of the slope. The safety coefficients obtained by the analytical method vary between 0.534 and 1.086, while those obtained by the numerical met

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Koffi, J. AGBELELE, C. HOUEHANOU Ernesto, Ferdinand AHLINHAN Marx, W. ALI Abdoul, and Comlan Aristide Houngan. "Assessment of Slope Stability by the Fellenius Slice Method: Analytical and numerical approach." World Journal of Advanced Research and Reviews 18, no. 2 (2023): 1205–14. https://doi.org/10.5281/zenodo.8414229.

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Slope stability is a topic of great importance in civil engineering, as slope failures can cause considerable damage to infrastructure and downstream properties. In this study, we applied the Fellenius slice method, using both the analytical method, as well as the numerical method, which was performed using the SLOPE/W module of the Geostudio software. The results obtained by both methods showed that the increase in soil cohesion improves the stability of the slope. The safety coefficients obtained by the analytical method vary between 0.534 and 1.086, while those obtained by the numerical met

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Ozer, Okan, Halide Koklu, and Serap Resitoglu. "Application of the Asymptotic Taylor Expansion Method to Bistable Potentials." Advances in Mathematical Physics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/239254.

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A recent method called asymptotic Taylor expansion (ATEM) is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.

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Su, Hai Dong, and Yong Feng Qi. "A Novel Numerical Method for Computing Stress Intensity Factors." Applied Mechanics and Materials 204-208 (October 2012): 4486–89. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4486.

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Based on Numerical Manifold Method (NMM), a novel method is presented for computing Stress Intensity Factor (SIF) of cracks. The Williams expansions are employed as the analytical solutions in the mesh containing the crack tip. And high-order polynomial functions are used as the numerical solutions in the surrounding meshes. Then the SIFs are computed via combination of the numerical solutions and the analytical solutions. Meanwhile, the meshes in NMM need not conform to the physical boundaries including the crack edges, allowing the cracks arbitrarily align within the meshes. The given exampl

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