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  1. 2081

    Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method by Mubashir Qayyum, Imbsat Oscar

    Published 2021-01-01
    “…To check the validity and convergence of the proposed scheme (LSHPM), the modeled problems are also solved with the Fehlberg–Runge–Kutta method (RKF45) and homotopy perturbation method (HPM) and residual errors are compared with LSHPM. …”
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  2. 2082

    Numerical Solutions of Duffing Van der Pol Equations on the Basis of Hybrid Functions by M. Mohammadi, A. R. Vahidi, T. Damercheli, S. Khezerloo

    Published 2023-01-01
    “…Resolved governance equation using the Runge-Kutta fourth order algorithm with the stepping time 0.01 s via numerical solution. …”
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  3. 2083

    Reappraising double pendulum dynamics across multiple computational platforms by Sandy Herho, Faiz Fajary, Katarina Herho, Iwan Anwar, Rusmawan Suwarman, Dasapta Irawan

    Published 2025-02-01
    “…These were solved numerically using the efficient Runge-Kutta-Fehlberg method, implemented in Python, R, GNU Octave, and Julia, while runtimes and memory usage were extensively benchmarked across these environments. …”
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    Article
  4. 2084

    Chemical Reaction Effects on the Flow of Titanium Dioxide–Water in a Mixed Convective Nanofluid along an Inclined Plate in a Porous Medium by Md. Nasir Uddin, Kakali Chowdhury, Jannatul Ferdows Mim

    Published 2024-01-01
    “…With the aid of a system of governing partial differential equations, a set of nonlinear ordinary differential equations for taking into consideration nanofluid flow have been derived using appropriate matching transformations. The Runge–Kutta method, as well as the Nachtsheim and Swigert Shooting method, is applied to numerically resolve the group of subsequent nondimensionalized equations. …”
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  5. 2085

    Nonlinear Dynamic Characteristics of Multidisk Rod Fastening Rotor with Axial Unbalance Mass Distribution by Li Zhao, Haosui Zhang, Yibing Liu, Chao Zhou

    Published 2022-01-01
    “…The mass unbalance on different disks was used to simulate blade faults in different parts, and nonlinear factors such as oil film force and disk contact effect were considered. The fourth-order Runge-Kutta method was used to solve the model, and the spectrum and axis trajectory curves were obtained. …”
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  6. 2086

    Analysis of Dynamic Characteristics of Grease-Lubricated Tapered Roller Bearings by Zheng-Hai Wu, Ying-Qiang Xu, Si-Er Deng

    Published 2018-01-01
    “…The impacts of load, grease rheological properties, and temperature on the roller tilt and skew and the bearing slip were simulated by using the fourth-order Runge–Kutta method. The results show that the roller tilt angle in the unloaded zone is obviously larger than that in the loaded zone, while the roller skew angle in the unloaded zone is smaller than that in the loaded zone. …”
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  7. 2087

    Limit Analysis of Collapse Mechanisms for Tunnel Roofs Subjected to Pore Water Pressure: A Numerical Approach by Jing-jing Liu, Tie-lin Chen, Chang-ling Xie, Jian-hua Tian, Yu-xin Wei

    Published 2021-01-01
    “…Then, the numerical approach based on the Runge–Kutta algorithm and traversal search method is proposed to solve the complex equations. …”
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  8. 2088

    Effect of Activation Energy on Magnetized Couple Stress Fluid over an Inclined Stretching Permeable Cylinder by Suman Sharma, Shalini Jain

    Published 2025-05-01
    “…Subsequently, these transformed equations are solved using fourth order Runge-Kutta mechanism along with the shooting technique. …”
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  9. 2089

    Hierarchical Modeling and Dynamic Analysis of Hoist System in Electric Mining Shovel by Wei Sun, Jianan Du, Lintao Wang, Penglong Luan, Jie li

    Published 2018-01-01
    “…Under the ripple drive torque simulated by Simulink, the dynamic characteristics of the hoist system in time domain and frequency domain were obtained using numerical integration with the Runge–Kutta method in Matlab. At last, the model validity was verified by contrasting the responses under actual test and the model. …”
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  10. 2090

    Vortex-Induced Vibration of a Cable-Stayed Bridge by M. T. Song, D. Q. Cao, W. D. Zhu

    Published 2016-01-01
    “…The dynamic response of the cable-stayed bridge is calculated using Runge-Kutta-Felhberg method in MATLAB for two cases with and without geometric nonlinear terms. …”
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  11. 2091

    Analysis of linear eddy current brakes for maglev train using an equivalent circuit method by Jun Liu, Wei Li, Lijun Jin, Guobin Lin, Yan Sun, Zhiwei Zhang

    Published 2021-09-01
    “…The state equation derived from the circuit equations and the Newton's equations is solved using the Runge–Kutta method, from which the dynamic performance of the linear ECBS can be obtained. …”
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