Dynamical analysis of a mathematical model on the spread of diphtheria disease with vaccination completeness factors by Nailul Izzati, Nanndo Yannuansa, Imamatul Ummah, Dian Anisa Rokhmah Wati, Elly Indahwati, Silviana Maya Purwasih, Nur Kholis

“…The dynamical analysis method used is by analyzing the eigenvalues and numerical calculation, while numerical simulations employ Fourth Order Runge-Kutta Method. Results from the dynamical analysis and numerical simulations indicate that the disease-free equilibrium point is stable if basic reproduction number , and the endemic equilibrium point is feasible and stable if . …”
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Study on the Shock Wave Characteristics of Spherical and Cylindrical Explosives in Near-field Underwater Explosion by J. Yu, X. P. Zhang, J. Wang, Y. Hao, H. B. Mao

“…A spatial discretization of the system equations utilizes a fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme for reconstruction, whereas temporal discretization employs a third-order Total Variation Diminishing (TVD) scheme implemented via Runge–Kutta methods. Furthermore, the description of the detonation reaction incorporates a newly developed programmed burn model. …”
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A Multiregion Discrete-Time Epidemic Model of Mycobacterium tuberculosis Infections: An Optimal Control Approach by Rachid Bouajaji, Hassan Laarabi, Mostafa Rachik, Abdelhadi Abta

“…The numerical results associated with the multipoint boundary value problems are obtained based on the forward-backward sweep method combined with progressive-regressive Runge–Kutta fourth-order schemes.…”
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The Impact of Media Coverage and Curfew on the Outbreak of Coronavirus Disease 2019 Model: Stability and Bifurcation by Afrah K. S. Al-Tameemi, Raid K. Naji

“…Numerical simulation is carried out in applying the model to the sample of the Iraqi population through solving the model using the Runge–Kutta fourth-order method with the help of Matlab. …”
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A Design Method of Inland River Channel Based on Hydrodynamic Response of Ship by ZHANG Lei, FENG Shaoxiong, TAN Kun, GUO Tao, SONG Chengguo, CHU Xiumin, MIAO Yang

“…First of all, the secondary development is undertaken based on Fluent for the problem of ship-flow interaction, in which flow domain is simulated by using the finite volume method, and governing equations of ship are embedded through user defined function (UDF) and solved by using the fourth-order Runge-Kutta method. The dynamic mesh technique is adopted to update the changing computation domains. …”
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NON-INVASIVE FAULT DIAGNOSIS OF GEARBOX CRACK IN ELECTROMECHANICAL DRIVE SYSTEM BASED ON STATOR CURRENT SIGNAL ANALYSIS OF THREE-PHASE AC ASYNCHRONOUS MOTOR by BAI GuoZhen, WANG Lu, LI BingChu, WANG ShuangYuan

“…First, establish a motor-gear-load electromechanical coupling model, and use the potential energy method to calculate the variable meshing stiffness of the gear under different crack lengths and angles; Then, the electromechanical coupling model is numerically solved by Runge-Kutta method to analyze the dynamic response of motor current under the influence of time-varying meshing stiffness. …”
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Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method by Mubashir Qayyum, Imbsat Oscar

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

“…Resolved governance equation using the Runge-Kutta fourth order algorithm with the stepping time 0.01 s via numerical solution. …”
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Computational Role of Autocatalytic Chemical Reaction in the Dynamics of a Ternary Hybrid Nanofluid Past a Rotating Stretching Surface by Shreedevi Madiwal, N. B. Naduvinamani, J. K. Madhukesh, Umair Khan, Anuar Ishak, Raman Kumar, Md Irfanul Haque Siddiqui

“…The governing equations are transformed into the system of ordinary differential equations (ODEs) and numerically tackled with the help of the Runge–Kutta–Fehlberg 4th 5th (RKF45) order scheme. The outcomes of pertinent constraints on their respective profiles are illustrated through graphs. …”
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INFLUENCE OF THE TIME OF DISINHIBITION TO TRANSIENTS AND WEAR OF THE FRICTION LININGS IN AN ASYNCHRONOUS MOTOR by V. V. Solencov, V. V. Brel

“…Calculation of the system of differential equations was fulfilled by the Runge – Kutta method. The deceleration of the electromechanical brake at various speeds caused different time values and stopping distances. …”
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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

“…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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Nonlinear Dynamics Analysis of the Wind Turbine Gear Transmission System Considering Friction Effect by Xu Fan, Liu Wenbin, Zhang Haibo, Zhang Qiang, Wu Shijing, Wang Xiaosun, Duan Jiujun

“…After nondimensionalization, the dynamics differential equations are obtained. Runge-Kutta methods are adopted to solve equations and the nonlinear dynamic response of the wind turbine gear transmission system is acquired. …”
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DYNAMIC MODELING AND SIMULATION ANALYSIS OF A ROLLING BEARING-ROTOR SYSTEM by LV Yun, TONG DaPeng, TIAN Ye, LAI YaHui

“…Use the way of variable step size "Runge-kutta"to make a solution through the model of dynamic. …”
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Artificial neural networks analysis for non-newtonian nanofluid flow with variable viscosity and MHD effects in wire covering processes by Maria Altaib Badawi, Zeeshan, Nehad Ali Shah, Imed Boukhris, Adel Thaljaoui

“…The data acquisition for the proposed ANN-LMA is generated for parameters involved in the model WCS-TGNFF through Runge-Kutta method. The training, validation, and testing phases of ANN-LMA are employed to assess the results derived from WC-TGNFF across diverse scenarios, and a comparative analysis of the derived results is conducted against a reference dataset to evaluate the precision and efficacy of the proposed ANN-LMA framework in addressing non-Newtonian fluid challenges associated with WC-TGNFF. …”
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Estimation of Surface Runoff for Al-Ghadaf Valley using the SWAT Model by Atheer G. Ibrahim

“…The area of the catchment was 8567.25  and the weather data used in this model was for three actual stations, Rutba, Ramadi, and Al-Nukhaib, for 13 years from 2009 to 2022. …”
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Nonlinear vibration analysis of a 3DOF double pendulum system near resonance by Asmaa Amer, W. Zhang, T.S. Amer, H. Li

“…These solutions are ascertained by contrasting them with numerical solutions (NS) that are derived utilizing the fourth-order Runge-Kutta algorithm (RKA-4). The modulation equations are constructed, and the principal external resonance cases are scrutinized concurrently based on the solvability constraints. …”
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Endothermic and exothermic reactions and stagnation point nanofluid flow over a porous stretched surface with a revised Buongiorno model by R.P. Ashrith, K.V. Nagaraja, P. Nimmy, Pinank Patel, Ankur Kulshreshta, J.K. Madhukesh, Chander Prakash

“…The fourth fifth-order scheme of the Runge Kutta Fehlberg method approach was used to solve the PDEs after they were converted into ODEs using similarity variables. …”
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A Numerical Approach to Study Ablation of Large Bolides: Application to Chelyabinsk by Josep M. Trigo-Rodríguez, Joan Dergham, Maria Gritsevich, Esko Lyytinen, Elizabeth A. Silber, Iwan P. Williams

“…To do that, we implemented a numerical (Runge–Kutta) method appropriate for deriving the ablation properties of bolides based on observations. …”
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Bioinformatics analysis and identification of underlying biomarkers potentially linking allergic rhinitis and autophagy by Tao Zhou, Hua Cai, Lisha Wu, Jianjun Chen, Liuqing Zhou, Jun Liu

“…A PPI network of differentially expressed autophagy-related genes were established and further identified through the CytoHubba algorithm. A receiver operating characteristic curve analysis was employed to evaluate the diagnostic effectiveness of the hub genes and to examine the relationship between autophagy-related genes and AR. …”
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Impact of the nonlinear thermal radiation on the Arrhenius activation energy of tangent hyperbolic micropolar hybrid nanofluid flow across an extending surface by MD. Shamshuddin, Balasani Srinitha, S.O. Salawu, M. Sunder Ram

“…The system of PDEs is transmuted into a dimensionless form of ODEs (ordinary derivative equations), which are then further treated with the MAPLE package based on the Runge-Kutta 4th order with shooting procedure. The influence of diverse terms on flow fields was examined via plotted graphs. …”
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