Dynamics Characteristic Analysis of Involute Gear with Asymmetric Tooth Considering the Influence of Time-varying Stiffness and Backlash by Qi Chen, Zhigang Yao, Yadong Wang, Yanming Wu

“…The time history chart， phase diagram， Poincaré perception map and FFT spectrogram are obtained by Runge-Kutta method， then the dynamics behaviors of gear with time-varying stiffness and changing backlash are analyzed. …”
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Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions by M. G. Sobamowo, A. T. Akinshilo, A. A. Yinusa

“…In order to verify the accuracy of the developed analytical solutions, the results of the homotopy perturbation method are compared with the results of the numerical method using the shooting method coupled with the fourth-order Runge–Kutta, and good agreements are established. Through the approximate analytical solutions, parametric studies are carried out to investigate the effects of nanoparticle size and shape, Brownian motion parameter, nanoparticle parameter, thermophoresis parameter, Hartmann number, Lewis number and pressure gradient parameters, slip, and temperature jump boundary conditions on thermo-solutal and hydromagnetic behavior of the nanofluid. …”
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Solving Parabolic and Hyperbolic Equations with Variable Coefficients Using Space-Time Localized Radial Basis Function Collocation Method by Mohammed Hamaidi, Ahmed Naji, Ahmed Taik

“…A comparison to the fourth-order Runge-Kutta method is also investigated.…”
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Analyzing Vibration Mechanism of Angular Contact Ball Bearing with Compound Faults on Inner and Outer Rings by Lihai Chen, Ma Fang, Ming Qiu, Yanfang Dong, Xiaoxu Pang, Junxing Li, Chuanmeng Yang

“…The step-changing fourth-order Runge–Kutta method is used to solve the dynamic compound fault model. …”
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Measurement System of Gear Dynamic Transmission Error based on Optical Encoder by Liang Zhihao, Zhao Kegang, Liu Yanwei, Ye Jie

“…The nonlinear dynamics model of a gear system is built and it’s solved based on fourth-order Runge-Kutta method. The simulation results（ rotation angles） are sampled by simulating the optical encoder and data acquisition card and the influence of the resolution of the optical encoder and the time resolution of the data acquisition card on the measurement accuracy is studied. …”
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DRIVING THE MINORITY AND MAJORITY INTERRELIGIOUS RELATIONS IN BALI by Titin Nurhidayati, Muhammad Bahrul Ula

“…The locus of this research is Jimbaran Village, South Kuta District, Badung Regency, Bali Province. This study uses a qualitative research methodology with a narrative descriptive analysis approach and is included in the type of literature study research. …”
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Hz. Peygamber Döneminden Günümüze Kadınlar ve Cami Eğitimi by Hüseyin YILMAZ

“…Günümüzde ise, erkek cemaatin camilerde sunulan hutbe, vaaz ve diğer etkinlikler yoluyla önemli ölçüde yaygın din eğitimi hizmeti aldığı, ancak kadınların cami eğitiminden yeterince yararlanamadığı görülmektedir. …”
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Thermal effects of ternary Casson nanofluid flow over a stretching sheet: An investigation of Thomson and Troian velocity slip by Musharafa Saleem, A. Al-Zubaidi, Neyara Radwan, S. Saleem, Hind Adawi

“…This leads to a set of partial differential equations (PDEs) based mathematical models transformed into ordinary differential equations (ODEs)-appropriate similarity transformation. The Runge–Kutta–Fehlberg (RKF-45) method solves the given ordinary differential system. …”
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Stability and computational analysis of Influenza-A epidemic model through double time delay by Ateq Alsaadi, Ali Raza, Muhammed Bilal Riaz, Umar Shafique

“…Both standard and nonstandard methods—such as Euler, Runge-Kutta, and nonstandard finite difference with a delayed sense—are presented to make computational analysis support a dynamical analysis and the best visualization of results. …”
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Protein Kinase A Is Involved in Neuropathic Pain by Activating the p38MAPK Pathway to Mediate Spinal Cord Cell Apoptosis by Yajun Deng, Liang Yang, Qiqi Xie, Fengbiao Yang, Guoqiang Li, Guangzhi Zhang, Shaoping Li, Zuolong Wu, Jing Wang, Xuewen Kang

“…A neuropathic pain-related gene expression dataset was downloaded from Gene Expression Omnibus, and differentially expressed genes were screened using the R software. cytoHubba was used to screen for hub genes. A spared nerve injury (SNI) rat model was established, and the paw withdrawal threshold was determined using von Frey filaments. …”
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Effect of Tooth Surface Friction on Bending Torsional Axial Pendular Coupling Nonlinear Amplitude Frequency Characteristic of Marine Herringbone Gear by Haoqin Zhang, Hao Dong, Libang Wang, Xiaolong Zhao

“…In the model， the friction coefficient， friction force and friction moment are calculated by using the elastohydrodynamic lubrication theory. The Runge-Kutta numerical method is used to solve the differential equation. …”
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Viscous heating of hybridized hydromagnetic MWCNTs-Fe3O4/water nanomaterial in a moving disk with non-uniform thermal model by S.O. Salawu, T.A. Yusuf, E.O. Fatunmbi, A.M. Obalalu

“…A similarity transformation of the governing model is done and solved by coupling a numerical shooting technique with a Runge–Kutta scheme. The tabulated and graphically presented results reveal that the thermal propagation rate is improved by 21.34% as 0.25 volume of NWCNTs-Fe3O4 nanoparticle is distributed in 0.5 volume of H2O solvent. …”
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Exploring damped and undamped frequencies in beam structures with viscoelastic supports using GFEM and state-space formulation by Gulnaz Kanwal, Hani Alahmadi, Rab Nawaz, Tayyab Nawaz

“…Additionally, the study introduces the application of state-space formulations combined with the Runge–Kutta method (RK4) to precisely analyze the response of damped systems, which adds significant value in exploring complex beam dynamics. …”
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Linearized Harmonic Balance Method for Seeking the Periodic Vibrations of Second- and Third-Order Nonlinear Oscillators by Chein-Shan Liu, Chung-Lun Kuo, Chih-Wen Chang

“…The LHBM can achieve quite accurate periodic solutions, whose accuracy is assessed by using the fourth-order Runge–Kutta numerical integration method. The optimal value of weight factor is chosen such that the absolute error of the periodic solution is minimized.…”
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Trihybrid nanofluid flow through nozzle of a rocket engine: Numerical solution and irreversibility analysis by Basharat Ullah, Rabia Rehman, Hafiz Abdul Wahab, Umar Khan, Walid Emam

“…We solve the altered equations using a shooting technique and the reduced Kutta-4 (RK-4) numerical method. With a particular focus on the Nusselt number and entropy generation number, graphic representations highlight the important parameters affecting hydrothermal performance. …”
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Precision optimization of reactive squeezing flow in stratified fluids: A response surface exploration by Anum Shafiq, Tabassum Naz Sindhu, Muhammad Ahmad Iqbal

“…The non-linear governing system is solved numerically using the Runge–Kutta fourth-order method (RK-4) combined with the shooting technique. …”
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Multi-Objective Optimal Design of Dropping Shock of Series Cushioning Packaging System by Yang Xue, Wei-Sheng Song, Hong-Tao Miao, Jing Wang, Yu Li

“…Based on the trained constitutive network model, the dynamic equation of the system is established, and the Runge-Kutta algorithm is utilized to resolve it. The multi-objective optimization (MOP) model of the series cushioning system is established for the first time. …”
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NONLINEAR CHARACTERISTICS OF HERRINGBONE GEAR FOUR-BRANCHING TRANSMISSION CONSIDERING GEAR BACKLASH EFFECT by DONG Hao, FANG ZongDe, FANG Zhou, ZHAO XiaoLong

“…With herringbone gear loaded tooth contact method of simulation technology,put forward a method for accurate calculation of herringbone gear meshing stiffness excitation; By using the theory of the concentrated parameter,three-dimensional dynamic model of bending torsion coupling of the system is established;Based on the dynamic differential equations are solved with variable step four order Runge-Kutta method,obtained under the influence of backlash in the system without impact,dynamic load coefficient and amplitude of unilateral and bilateral shock state.The results show that Power four branch transmission system has a complex nonlinear characteristic,which is sensitive to the change of the tooth side gap,the influence of the backlash on the nonlinear characteristics is greater,and the system load changes from the side impact to the side impact of the system when the backlash is changed from 0 μm 150 μm; When the tooth gap is greater than a certain critical value,the dynamic characteristics of the system will not change with the increase of the gap of the tooth. …”
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Entropy optimization of stagnant blood flow systems with tetra-hybrid nano additives under viscous dissipation, joule heating and thermal radiation effects by Meena Rajeswari P, Poulomi De

“…Numerical solutions are obtained by Runge-Kutta-Fehlberg 5th order method with shooting strategy. …”
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Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials by Luc Leroy Mambou Ngueyep, Joseph Ndop, Elise Rose Atangana Nkene, Jean-Marie Bienvenu Ndjaka

“…The calculations performed have allowed finding an analytical solution which was compared with numerical solutions obtained by using the shooting method and the fourth-order Runge-Kutta algorithm. These analytical and numerical results have shown that the values of tangential stresses are greater than the radial stresses. …”
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