Numerical Treatment of the Model for HIV Infection of CD4+T Cells by Using Multistep Laplace Adomian Decomposition Method by Nurettin Doğan

“…The proposed method is modification of the classical Laplace Adomian Decomposition Method (LADM) with multistep approach. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. …”
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Numerical Investigation of Contact Burning in an Air-Breathing Continuous Rotating Detonation Engine by Dapeng Xiong, Mingbo Sun, Haoyang Peng, Yanan Wang, Yixin Yang, Hongbo Wang, Jiangfei Yu, Zhenguo Wang

“…The second-order upwind advection upstream splitting method and second-order Runge-Kutta method are used to discretize space and time terms, and detailed 9-species 19-step hydrogen-oxygen reactions are applied in this study. …”
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Thermal radiation effect on MHD stagnation point flow with partial slip by Praveen Kumar Dadheech, Navin Kumar, Priyanka Agrawal, Qasem Al-Mdallal

“…Then the transformed set of equations of the flow after applying suitable similarity solutions were encountered by Shooting Technique in conjunction with the fourth ordered Runge-Kutta method. Numerical solutions with graphical representation are studied. …”
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Study on the Influence of Tooth Surface Friction on Bifurcation Characteristic of Multiple Clearance Bending and Torsion Coupling Gear by Liu Zhiyu Liu Bo Dong Hao

“…In order to study the gear bifurcation characteristic under the influence of tooth surface friction, based on the lumped parameter theory, considering the non-linear factors such as tooth surface friction, time-varying meshing stiffness, gear backlash and bearing clearance, a six-degree-of-freedom bending-torsion coupled vibration model of gear pairs is established. The Runge-Kutta numerical method is used to solve the model, and the influence of tooth surface friction on the bifurcation characteristics of the system is analyzed with various parameters. …”
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Non-oscillatory central schemes for the Saint-Venant system by Rooholah Abedian

“…The proposed method combines a Runge-Kutta scheme for accurate time integration and the natural continuous extension method for spatial discretization. …”
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Nonlinear Frequency Response Analysis of Herringbone Gear Pair based on Incremental Harmonic Balance Method by Libang Wang, Hao Dong

“…The frequency response characteristics of the system under constant and dynamic backlashes are solved by incremental harmonic balance method， and the results are further verified by Runge-Kutta numerical integration method. The influence of time-varying meshing stiffness， damping， static transmission error and external load excitation on the amplitude frequency characteristics of the system is analyzed. …”
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Dynamic Load Performance of a Face Gear Drive in a Spent Fuel Reactor by Guo Mingchao, Zhang Ju, Xu Lei, Kan Chen

“…The dynamic model of the face gear drive is established based on the centralized mass method.The influence of factors such as manufacturing errors and misalignments, time-varying meshing stiffness, corrosion on tooth surfaces, earthquakes on the dynamic performance are taken into consideration to deduce the differential equations of the face gear drive. Runge-Kutta method is applied to solve the differential equation, the dynamic loads under excitations of misalignment, earthquake and corrosion are obtained, and the influence law of these excitations on the dynamic load coefficient is further analyzed. …”
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Study on the Load Sharing Characteristic and Influential Factor of the Planetary Transmission of Vertical Mill Reducer by Wang Wuguang

“…Taking planetary gear pair time-meshing stiffness,meshing damping,bearing support stiffness,support damping of vertical mill reducer into consideration,the vibration differential equation of planetary gear transmission is set up based on lumped parameter method,the dynamic mesh force of each gear pair is obtained by adopting Runge-Kutta method. The sun gear of no floating and eccentricity error of sun gear,planet gear,gear ring are studied to get its effect on planetary transmission load sharing characteristic. …”
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Performance Analysis and Comparison for High Maneuver Target Track Based on Different Jerk Models by Qinghai Meng, Bowen Hou, Dong Li, Zhangming He, Jiongqi Wang

“…The simplified dynamic model is used to gain the standard trajectory with Runge-Kutta numerical integration method. The mathematical simulations show that Jerk model with self-adaptive noise variance has the best robustness while other models may diverge when the initial error is much larger. …”
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Nonlinear Vibration Analysis of Rotor considering Cogging and Harmonic Effects by Shanle Li, Feng Liu, Hongyan Wang, Haijun Song, Kuilong Yu

“…Motion equations of rotor system were established, and Runge–Kutta method was used to solve the equations. Results showed that errors between finite and analytical results were smaller considering cogging and harmonic effects. …”
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Some Novel Solutions to a Quadratically Damped Pendulum Oscillator: Analytical and Numerical Approximations by Alvaro H. Salas, Wedad Albalawi, M. R. Alharthi, S. A. El-Tantawy

“…Several examples are discussed and compared to the Runge–Kutta (RK) numerical approximation to investigate and examine the accuracy of the obtained approximations. …”
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Dynamic Analysis of Flexible Shaft and Elastic Disk Rotor System Based on the Effect of Alford Force by Wenjun Yang, Huiqun Yuan, Li Hui, Kaifeng Zhang

“…Taken the flexible shaft and elastic disk rotor system as the research object, vibration differential equations are established by the modal synthesis method. Based on the Runge–Kutta method of direct integration, dynamic equations are solved successfully. …”
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DYNAMIC CHARACTERISTICS OF A COLLISION SYSTEM WITH DRY FRICTION AND NONLINEAR CONSTRAINTS (MT) by MA Shuo, ZHU XiFeng, WANG JianFeng

“…Through the fourth-order variable step Runge-Kutta numerical algorithm, the dynamics of the mechanical vibration system generated by the low-frequency excitation of the p/1 periodic motion are analyzed. …”
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Coupling Research on Lubrication and Gear Dynamics Under Different-carrier Ferrofluids by Ren Fenglan, Wei Kun, Jian Guangxiao, Wang Youqiang

“…Based on the fourth order Runge-Kutta method, the multi-grid method and multi-grid integration method, the influence of different-carrier ferrofluids on oil film and the distribution of dynamic loads are analyzed. …”
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Combined Effect of Buoyancy Force and Navier Slip on MHD Flow of a Nanofluid over a Convectively Heated Vertical Porous Plate by Winifred Nduku Mutuku-Njane, Oluwole Daniel Makinde

“…A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration. …”
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Identification and verification of autophagy-related gene signatures and their association with immune infiltration and drug responsiveness in epilepsy by Han-han He, Xiao-ge Zhang, Fen-fang Chen

“…The hub ARDEGs were identified through CytoHubba, followed by the LASSO analysis. The Immune Cell Abundance Identifier (ImmuCellAI) was used to estimate peripheral immune cells abundance of epilepsy. …”
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Dynamic Analysis of a Rotor-Bearing-SFD System with the Bearing Inner Race Defect by Junhong Zhang, Xin Lu, Jiewei Lin, Liang Ma, Jun Wang

“…The equations of motion of the rotor-bearing-SFD system are derived and solved using the fourth-order Runge-Kutta method. The dynamic behavior and the fault characteristics are analyzed with two configurations of the SFD: (1) mounted on the unfaulted bearing and (2) mounted on the faulty bearing. …”
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Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode by Harun-Or-Roshid, Alrazi Abdeljabbar, Md․ Sabur Uddin, Mst․ Shekha Khatun

“…By tracing the trajectory of each phase portrait, we obtain a range of numerical solutions utilizing the fourth-order Runge-Kutta method. Quasi-periodic and chaotic natures of the model extract for additional forcing term of the mode. …”
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Heat Transfer in Boundary Layer Magneto-Micropolar Fluids with Temperature-Dependent Material Properties over a Stretching Sheet by Ephesus O. Fatunmbi, Samuel S. Okoya

“…With the aid of similarity conversion analysis, the formulated equations of the flow and heat transfer have been translated into a system of nonlinear ordinary differential equations. Subsequently, Runge–Kutta–Fehlberg integration scheme in company of shooting techniques employed to obtain numerical solutions to the reduced equations. …”
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The Analysis of Secondary Motion and Lubrication Performance of Piston considering the Piston Skirt Profile by Yanjun Lu, Sha Li, Peng Wang, Cheng Liu, Yongfang Zhang, Norbert Müller

“…The secondary motion of piston-connecting rod system is modeled; the trajectory of the piston is calculated by the Runge-Kutta method. By considering the inertia of the connecting rod, the influence of the longitudinal and horizontal profiles of piston skirt, the offset of the piston pin, and the thermal deformation on the secondary motion and lubrication performance is investigated. …”
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