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Journal articles on the topic 'Euler's Method'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Singh, Ravindra, Omwati Rana, Yogesh Kumar sharma, and Shiv Shankar Gaur. "Numerical Approximation Methods and Comparison with RK-4 Method for a Linear Differential Equation with Initial Conditions Using Scilab 6.1.1." Current Natural Sciences and Engineering 1, no. 6 (2024): 471–79. https://doi.org/10.63015/5c-2447.1.6.

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Numerical approximation methods have been developed to linear differential equation with initial condition. The comparison of the results has been done among Euler’s method, modified Euler’s method and RK-4 with the help of Scilab software 6.1.1. RK-4 method is effective enough to reach more accuracy in the result. The Runge-Kutta method attempts to overcome the problem of the Euler's method, and modified Euler's method and the study shows that in all cases RK-4 method improves to a great extent, than those by the Euler method and Modified Euler’s Method. For RK-4 the approximation accuracy is

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2

A. Hari Ganesh. "An Enhanced Euler's Methods Based on Heronian and Cubic Means for Numerically Solving Fuzzy Differential Equations." Advances in Nonlinear Variational Inequalities 28, no. 4s (2025): 431–52. https://doi.org/10.52783/anvi.v28.3501.

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Introduction: In recent years, fuzzy differential equations have become an increasingly popular topic. In engineering and scientific fields, the study of numerical solutions for fuzzy differential equations is crucial. For the purpose of solving fuzzy initial value problems, several numerical approaches have been devised. Objectives: This attempt aims to create enhanced Euler's methods for numerically solving fuzzy differential equations to generate approximate solutions for situations too complex to be expressed precisely. Methods: Euler's Method, Modified Euler's Method, and Improved Euler's

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3

Albertino de Jesus. "Collaboration Between Private Universities and the Government in Advancing Human Resources Based on the "Spirit of Maubereism" in Timor-Leste." Communications on Applied Nonlinear Analysis 32, no. 8s (2025): 285–301. https://doi.org/10.52783/cana.v32.3671.

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Objectives: Fuzzy differential equations (FDEs) are crucial for modeling dynamic systems in science, economics, and engineering due to their unpredictable nature and the need for numerical methods for precise solutions. The objective of this work is to develop improved Euler's techniques for numerically solving fuzzy differential equations (FDEs) in order to produce approximate solutions for problems that are too complicated to be stated exactly. Methods: This study proposes improved Euler's approaches for solving differential equations with fuzzy initial conditions, including Euler's Method,

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4

A. Hari Ganesh. "A Numerical Approach for Solving Fuzzy Differential Equation Using Enhanced Euler’s Methods Based on Contra Harmonic Mean and Centroidal Mean." Communications on Applied Nonlinear Analysis 32, no. 8s (2025): 271–84. https://doi.org/10.52783/cana.v32.3670.

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Objectives: Fuzzy differential equations (FDEs) are crucial for modeling dynamic systems in science, economics, and engineering due to their unpredictable nature and the need for numerical methods for precise solutions. The objective of this work is to develop improved Euler's techniques for numerically solving fuzzy differential equations (FDEs) in order to produce approximate solutions for problems that are too complicated to be stated exactly. Methods: This study proposes improved Euler's approaches for solving differential equations with fuzzy initial conditions, including Euler's Method,

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5

LAWSON, D. A. "Potential Perils of Euler's Method." Teaching Mathematics and its Applications 14, no. 2 (1995): 83–85. http://dx.doi.org/10.1093/teamat/14.2.83.

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6

Sălăjan (Pomian), Raluca Anamaria. "The convergence of the Euler's method." Journal of Numerical Analysis and Approximation Theory 39, no. 1 (2010): 87–92. http://dx.doi.org/10.33993/jnaat391-922.

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In this article we study the Euler's iterative method. For this method we give a global theorem of convergence. In the last section of the paper we give a numerical example which illustrates the result exposed in this work.

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7

Byers, R. M. "Time Optimal Attitude Control of Asymmetric Rigid Spacecraft." Journal of Vibration and Control 2, no. 1 (1996): 17–32. http://dx.doi.org/10.1177/107754639600200102.

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Time optimal rest-to-rest reorientation of a rigid spacecraft with an arbitrary initial attitude and distinct principal moments of inertia is discussed. The effect of the gyroscopic coupling terms in Euler's equations on the control switch times is shown. A method for recursively generating coefficients for a truncated Taylor series solution of Euler's equations and the differential equations for the Euler parameter state transition matrix is shown. These solutions are used to solve for the optimal control switch times.

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8

Domokos, G., and P. Holmes. "Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling." Journal of Nonlinear Science 3, no. 1 (1993): 109–51. http://dx.doi.org/10.1007/bf02429861.

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9

Domokos, G., and P. Holmes. "Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling." Journal of Nonlinear Science 3, no. 1 (1993): 267. http://dx.doi.org/10.1007/bf02429866.

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10

Borges, Carlos F. "Discretization vs. Rounding Error in Euler's Method." College Mathematics Journal 42, no. 5 (2011): 396–99. http://dx.doi.org/10.4169/college.math.j.42.5.396.

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11

Donahue, Steven, and Thomas J. Osler. "96.09 Euler's method of integration by parts." Mathematical Gazette 96, no. 535 (2012): 115–16. http://dx.doi.org/10.1017/s0025557200004095.

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12

Nupur, Sanjida, Reshma Akter, Tashmir Reza Tamanna, and Parvin Akter. "Maximizing Accuracy: Advancements in Numerical Methods for Ordinary Differential Equations." Aug-Sept 2023, no. 35 (July 18, 2023): 18–27. http://dx.doi.org/10.55529/jecnam.35.18.27.

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Euler’s Method, Taylor’s Method are the most fundamental and easiest methods to solve first order ordinary differential equations (ODEs). Many other methods like Runge-Kutta Method have been developed on the basis of these method. In this paper, the basic ideas behind Euler's Method, Taylor's Method, and Runge-Kutta Method, as well as the geometrical interpretation have been discussed. The main focus is confined to the mathematical interpretation and graphical representation of these method and to find a way to reduce the errors. In order to verify the accuracy of these methods, we compare num

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13

Abdel Rahman, Abdel Radi Abdel Gadir, Neama Yahia Mohammed, Subhi Abdalazim Aljily, and Nidal Elamen Mohammed Ali. "On Infinite Series and with Their Some Applications to Euler's Summation Formula." European Journal of Mathematics and Statistics 2, no. 3 (2021): 25–31. http://dx.doi.org/10.24018/ejmath.2021.2.3.32.

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Infinite series is still used in engineering, mathematical and physical sciences.In the modern area a great progress is made in the sciences of calculus in addition to what was accompanied by advances in infinite series and their some applications .The aims of this paper is to develop and introduces the infinite series and their some applications to Euler's summation , also we show and explain how to apply the infinite series in Euler's summation .We followed the induction mathematical method and found that : The relationship through the Euler's summation focused on the physical link questione

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14

Ruaa N. Abduallah and Rokan khaji. "Numerical Studied for Solving Fuzzy Integro-Differential Equations via Caputo Fractional Derivative." Academic Science Journal 2, no. 4 (2024): 228–40. http://dx.doi.org/10.24237/asj.02.04.780b.

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In this paper, we extended some numerical methods to solve fuzzy integro differential equations. The considered problem involves the fractional Caputo derivatives under some conditions on the ordered. As we combine Euler's method with composite Simpsons have been used to determine the solutions of these equations. We extend these numerical techniques to find the best solutions. Extended difference Euler technique is used for this. The results show that the extended Euler method is more accurate in terms of absolute error. Illustrative examples are given to demonstrate the high precision and go

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15

Yu, Hui, and Minghui Song. "Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/675781.

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The numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler's method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. The main aim is to investigate the convergence of the Euler method in probability to such equations with non-Lipschitz coefficients. Numerical example is given to demonstrate our results.

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16

Kanwar, V., and S. K. Tomar. "Exponentially fitted variants of Euler's method for ODEs." International Journal of Mathematical Education in Science and Technology 39, no. 8 (2008): 1112–16. http://dx.doi.org/10.1080/00207390802357810.

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17

TAKASE, Syouta, and Manabu KOSAKA. "G101091 A study on destabilization by Euler's method." Proceedings of Mechanical Engineering Congress, Japan 2013 (2013): _G101091–1—_G101091–4. http://dx.doi.org/10.1299/jsmemecj.2013._g101091-1.

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18

Mckee, James. "Turning Euler's Factoring Method into a Factoring Algorithm." Bulletin of the London Mathematical Society 28, no. 4 (1996): 351–55. http://dx.doi.org/10.1112/blms/28.4.351.

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19

Nickalls, R. W. D. "The quartic equation: invariants and Euler's solution revealed." Mathematical Gazette 93, no. 526 (2009): 66–75. http://dx.doi.org/10.1017/s0025557200184190.

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The central role of the resolvent cubic in the solution of the quartic was first appreciated by Leonard Euler (1707-1783). Euler's quartic solution first appeared as a brief section (§ 5) in a paper on roots of equations [1, 2], and was later expanded into a chapter entitled ‘Of a new method of resolving equations of the fourth degree’ (§§ 773-783) in his Elements of algebra [3,4].

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20

Brasselet, Jean-Paul, and Nguyn̂̃n Thị Bích Thủy. "An elementary proof of Euler's formula using Cauchy's method." Topology and its Applications 293 (April 2021): 107558. http://dx.doi.org/10.1016/j.topol.2020.107558.

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21

Duan, Yuping. "A Fast Augmented Lagrangian Method for Euler's Elastica Models." Numerical Mathematics: Theory, Methods and Applications 6, no. 1 (2013): 47–71. http://dx.doi.org/10.4208/nmtma.2013.mssvm03.

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22

Zhang, Jun, Rongliang Chen, Chengzhi Deng, and Shengqian Wang. "Fast Linearized Augmented Lagrangian Method for Euler's Elastica Model." Numerical Mathematics: Theory, Methods and Applications 10, no. 1 (2017): 98–115. http://dx.doi.org/10.4208/nmtma.2017.m1611.

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AbstractRecently, many variational models involving high order derivatives have been widely used in image processing, because they can reduce staircase effects during noise elimination. However, it is very challenging to construct efficient algorithms to obtain the minimizers of original high order functionals. In this paper, we propose a new linearized augmented Lagrangian method for Euler's elastica image denoising model. We detail the procedures of finding the saddle-points of the augmented Lagrangian functional. Instead of solving associated linear systems by FFT or linear iterative method

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23

Princewill Nnamdi OKECHUKWU, Williams Nirorowan OFUYAH, and Ajirioghene Moses OGUH. "Basement depths estimation using the Euler-3D and source parameter imaging methods from the analysis of ground magnetic field data in the Niger Delta Basin." International Journal of Science and Research Archive 14, no. 1 (2025): 218–29. https://doi.org/10.30574/ijsra.2025.14.1.2385.

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This study estimates basement depths in the Niger Delta Basin using ground magnetic field data, analysed through Euler-3D deconvolution and Source Parameter Imaging (SPI) methods. Ground magnetic data were collected with an AMC-6 High-precision Fluxgate Magnetometer across 6 dip and 14 strike profiles, alongside a tie-line. The Euler-3D deconvolution method was applied to map the depth and distribution of magnetic sources by solving Euler's homogeneity equation, while the SPI method provided an independent depth estimate using the local wavenumber approach. Both methods revealed significant ba

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24

Mazhouda, Kamel. "The Saddle-Point Method and the Li Coefficients." Canadian Mathematical Bulletin 54, no. 2 (2011): 316–29. http://dx.doi.org/10.4153/cmb-2011-016-6.

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AbstractIn this paper, we apply the saddle-point method in conjunction with the theory of the Nörlund–Rice integrals to derive precise asymptotic formula for the generalized Li coefficients established by Omar and Mazhouda. Actually, for any function F in the Selberg class and under the Generalized Riemann Hypothesis, we havewithwhere γ is the Euler's constant and the notation is as below.

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25

Suryo, Widodo, Agus Sulistyono Bambang, and Katminingsih Yuni. "Numerical Simulation of Infectious Disease Spread Using the SIR Model: an Application of Euler's Method." International Journal of Mathematics and Computer Research 13, no. 02 (2025): 4894–98. https://doi.org/10.5281/zenodo.14929055.

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The spread of infectious diseases is a very complex phenomenon and requires mathematical modeling to understand the dynamics of the spread. One of the common approaches used to model the spread of diseases is the SIR (Susceptible-Infected-Recovered) model. This study aims to implement numerical methods, especially the Euler method, to simulate the spread of infectious diseases using the SIR model. This study focuses on the application of Euler's Method to solve differential equations that describe the changes in infected, susceptible, and recovered populations in a finite system. The Euler met

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26

Le Coënt, Adrien, Florian De Vuyst, Ludovic Chamoin, and Laurent Fribourg. "Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method." Electronic Proceedings in Theoretical Computer Science 247 (April 8, 2017): 18–33. http://dx.doi.org/10.4204/eptcs.247.2.

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27

Prentice, Justin Steven Calder. "Evaluating a double integral using Euler's method and Richardson extrapolation." Lietuvos matematikos rinkinys 65 (December 10, 2024): 39–52. https://doi.org/10.15388/lmd.2024.38091.

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We transform a double integral into a second-order initial value problem, which we solve using Euler's method and Richardson extrapolation. For an example we consider, we achieve accuracy close to machine precision (~10-13). We find that the algorithm is capable of determining the error curve for an arbitrary cubature formula, and we use this feature to determine the error curve for a Simpson cubature rule. We also provide a generalization of the method to the case of nonlinear limits in the outer integral.

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28

Orem, Hendrik. "Basins of Attraction and Perturbed Numerical Solutions using Euler's Method." SIAM Undergraduate Research Online 1, no. 2 (2008): 62–69. http://dx.doi.org/10.1137/08s010116.

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29

Boyd, John P. "A lag-averaged generalization of Euler's method for accelerating series." Applied Mathematics and Computation 72, no. 2-3 (1995): 143–66. http://dx.doi.org/10.1016/0096-3003(94)00180-c.

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30

T. F. A. Almajbri., S. S. M. abu-amr, and A. B. Mohammed. "NUMERICAL STUDIES FOR SOLVING ABEL'S DIFFERENTIAL EQUATION." Malaysian Journal of Industrial Technology 8, no. 4 (2024): 93–104. https://doi.org/10.70672/9641zr57.

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This paper uses the Abel's Equation, often used in various fields including physics and engineering, represents a mathematical model that can be complex to solve analytically. This research focuses on solving the Abel's Equation using several numerical methods: Euler's method, Taylor series method, Adomian decomposition method, and Runge-Kutta method. Each method has its advantages and applicability depending on the specific characteristics of the equation being solved.

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31

Zhao, Shibo. "The advantage of symplectic Euler in optimization and its application." Theoretical and Natural Science 10, no. 1 (2023): 230–34. http://dx.doi.org/10.54254/2753-8818/10/20230349.

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Many professions today place a high value on optimization, and many problems can eventually be transformed into optimization issues. There are many iterative methods available today to handle optimization issues, however many algorithms' design principles are unclear. Weijie Su solved this problem by discretizing the iterative equation using an ordinary differential equation, but different discretization techniques will provide different outcomes. So choosing an appropriate method is important. Three discretization techniquesexplicit Euler, implicit Euler, and symplectic Eulerare compared in t

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32

Lei, De Bao, Zhong Hua Tang, and Yan Hui Zheng. "Low Speed Preconditioning Algorithm Used in the Process of Calculating Euler Equation." Applied Mechanics and Materials 275-277 (January 2013): 451–55. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.451.

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This paper describes a numerical method for solving the unsteady Euler equation at any speed. In the process of calculating Euler's equation, the control equation in orthogonal curvilinear coordinate system is discretized by the finite -volume scheme based on the center-difference method, and convection flux used Jameson central deference scheme was solved at every pseudo time step, and the Runge-Kutta method, dual-time algorithm and the implicit LU-SGS add preconditioning algorithm are used for time-marching. For obtaining the numerical solution of two-dimensional unsteady flow around a cylin

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33

Paudel, Dharma Raj, and Mohan Raj Bhatta. "Comparative study of Euler's method and Runge-Kutta method to solve an ordinary differential equation through a computational approach." Academic Journal of Mathematics Education 6, no. 1 (2023): 81–85. http://dx.doi.org/10.3126/ajme.v6i1.63802.

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Euler’s and Runge-Kutta's methods are used to solve ordinary differential equations. Euler’s methods become appropriate method for solving the equations. When the steps are small, they give reasonably accurate results. However, if the steps are not so small, the Runge-Kutta method is preferred to solve the problem. This paper uses the Python program to show the results of both methods. This computational approach shows that the Runge-Kutta method is better for small steps at solving differential equations than Euler’s method.

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34

He, Fang, Xiao Wang, and Xiaojun Chen. "A Penalty Relaxation Method for Image Processing Using Euler's Elastica Model." SIAM Journal on Imaging Sciences 14, no. 1 (2021): 389–417. http://dx.doi.org/10.1137/20m1335601.

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35

Singh, Gurjinder, V. Kanwar, and Saurabh Bhatia. "A class of the backward Euler's method for initial value problems." Research Journal of Engineering and Technology 6, no. 1 (2015): 207. http://dx.doi.org/10.5958/2321-581x.2015.00031.8.

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36

Kulys, J. "Modeling of biological Kinetics by Euler's Method: solving mediator stability Problem." Nonlinear Analysis: Modelling and Control 1 (September 2, 1997): 67–70. http://dx.doi.org/10.15388/na.1997.1.0.15272.

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37

Tai, Xue-Cheng, Jooyoung Hahn, and Ginmo Jason Chung. "A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method." SIAM Journal on Imaging Sciences 4, no. 1 (2011): 313–44. http://dx.doi.org/10.1137/100803730.

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38

Edalat, Abbas, Amin Farjudian, Mina Mohammadian, and Dirk Pattinson. "Domain Theoretic Second-Order Euler's Method for Solving Initial Value Problems." Electronic Notes in Theoretical Computer Science 352 (October 2020): 105–28. http://dx.doi.org/10.1016/j.entcs.2020.09.006.

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39

Hayashi, H., and T. Mitsui. "Further analysis of stability for Lambert's method based on Euler's rule." Computers & Mathematics with Applications 31, no. 8 (1996): 31–36. http://dx.doi.org/10.1016/0898-1221(96)00028-4.

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40

Baier, Robert, Ilyes Aïssa Chahma, and Frank Lempio. "Stability and Convergence of Euler's Method for State-Constrained Differential Inclusions." SIAM Journal on Optimization 18, no. 3 (2007): 1004–26. http://dx.doi.org/10.1137/060661867.

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41

Kull, Trent C. "Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course." PRIMUS 21, no. 7 (2011): 638–50. http://dx.doi.org/10.1080/10511971003592436.

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42

Zhang, Jianying, and Bin Jiang. "Enhanced Euler's method to a free boundary porous media flow problem." Numerical Methods for Partial Differential Equations 28, no. 5 (2011): 1558–73. http://dx.doi.org/10.1002/num.20691.

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43

Zaiats, V., J. Majewski, T. Marciniak, and M. Zaiats. "The combination numerical method of effective processing high frequency signals." КОМП’ЮТЕРНО-ІНТЕГРОВАНІ ТЕХНОЛОГІЇ: ОСВІТА, НАУКА, ВИРОБНИЦТВО, no. 36 (November 21, 2019): 21–28. http://dx.doi.org/10.36910/6775-2524-0560-2019-36-4.

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An iterative approach to the construction of second-order numerical methods based on the Liniger-Willaby method with minimal error of discretization is proposed. The essence of the approach is to identify corrections to the Euler's explicit and implicit method at a time when their contributions to the amendment are equivalent. Improved time and accuracy in the process of determining the characteristics of quartz oscillators of the 9th order and high-speed auto-generators18 of the order with very long transients.

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44

S, Sindu Devi, and Ganesan K. "An Approximate Solution of Fuzzy Initial Value Problem through Euler's Modified Method." Journal of Advanced Research in Dynamical and Control Systems 12, no. 5 (2020): 281–85. http://dx.doi.org/10.5373/jardcs/v12i5/20201715.

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45

Dirbaz, Mohadese, and Fatemeh Dirbaz. "Numerical Solution of Impulsive Fuzzy Initial Value Problem by Modified Euler's Method." Journal of Fuzzy Set Valued Analysis 2016 (2016): 50–57. http://dx.doi.org/10.5899/2016/jfsva-00280.

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46

Lukshin, A. V., and S. N. Smirnov. "A stochastic algorithm for solving the Boltzmann equation based on Euler's method." USSR Computational Mathematics and Mathematical Physics 28, no. 3 (1988): 96–99. http://dx.doi.org/10.1016/0041-5553(88)90183-8.

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47

CAO, JIAN. "ALTERNATIVE PROOFS OF GENERATING FUNCTIONS FOR HAHN POLYNOMIALS AND SOME APPLICATIONS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 14, no. 04 (2011): 571–90. http://dx.doi.org/10.1142/s0219025711004511.

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In this paper, utilizing the moments representations of Hahn polynomials, we show how to derive their bilinear, trilinear and multilinear generating functions. Moreover, from Euler's finite q-differences, we deduce the q-Chu–Vandermonde formula and consider its generalizations by the moments method.

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48

Randhir, D., S. Umashankar, D. Vijayakumar, and D. P. Kothari. "Comparative Analysis of Solution Methods to Power Electronic Interface Modeling for Renewable Energy Applications." Advanced Materials Research 768 (September 2013): 9–15. http://dx.doi.org/10.4028/www.scientific.net/amr.768.9.

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This paper presents the comparison between various numerical methods namely Euler's Method, Midpoint Method, 2nd order Runge Kutta Method and 4th order Runge Kutta Method with the analytical method to solve a power electronic system in both single phase and three phase configuration using decoupled methodology. The values of source current, load current and DC link voltage are obtained for each method using Matlab software and compared with each other. Also, the error in each numerical method with respect to analytical method is calculated and tabulated. These power electronic models could be

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49

Kapçiu, Rinela, Brikena Preni, Eglantina Kalluçi, and Robert Kosova. "MODELING INFLATION DYNAMICS USING THE LOGISTIC MODEL: INSIGHTS AND FINDINGS." Jurnal Ilmiah Ilmu Terapan Universitas Jambi 8, no. 1 (2024): 364–78. http://dx.doi.org/10.22437/jiituj.v8i1.32605.

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This paper examines applying the logistic model, frequently used in biology, to analyze inflation patterns in dynamic economic systems. The primary objective is to simulate and analyze the complex dynamics of inflation, thus providing new insights into the stability of financial institutions. Numerical methods such as Euler's Method, Runge-Kutta Method (RK4), and Adams-Bashforth-Moulton's method were used to simulate inflation patterns by discretizing the logistic equation. The data utilized in this research were obtained from INSTAT, BoA, MoF, and Eurostat, with quarterly results from 1995 to

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50

Purczyński, Jan. "Simplified Method of GED Distribution Parameters Estimation." Folia Oeconomica Stetinensia 10, no. 2 (2012): 35–49. http://dx.doi.org/10.2478/v10031-011-0043-9.

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Simplified Method of GED Distribution Parameters EstimationIn this paper a simplified method of estimating GED distribution parameters has been proposed. The method uses first, second and 0.5-th order absolute moments. Unlike in maximum likelihood method, which involves solving a set of equations including special mathematical functions, the solution is given in the form of a simple relation. Application of three different approximations of Euler's gamma function value results in three different sets of results for which the χ2test is conducted. As a final solution (estimation of distribution

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