A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property by Ruifeng Wu, Huilai Li, Tieru Wu

“…Finally, applying our operators to the fitting of discrete solutions of initial value problems, we find that our method has smaller errors than the Runge-Kutta method of order 4 and Wang et al.’s quasi-interpolation scheme.…”
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ANALYSIS ON DYNAMIC CHARACTERISTICS OF TOOTH ROOT CRACK OF GEAR DRIVE SYSTEM UNDER VARIABLE LOAD EXCITATION by SHI PeiMing, ZHAO Na, LIANG Kai, HAN DongYing

“…According to the characteristics that crack can cause changes in mesh stiffness,the four degree of freedom dynamic model of the single-stage gear transmission system with the gear crack fault is established and the nonlinear dynamic mechanism of crack fault is studied. The Runge-Kutta numerical method was used to simulate and analysis crack fault. …”
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Reducing the Possibility of Ruin by Maximizing the Survival Function for the Insurance Company’s Portfolio by Masoud Komunte, Christian Kasumo, Verdiana Grace Masanja

“…This system was then solved numerically using the fourth-order Runge-Kutta method. The results show that the survival function increases with the increase in the intensity of the counting process but decreases with an increase in the instantaneous rate of stock return and return volatility. …”
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Nonlinear system optimization of cutting tools with dynamic vibration absorbers in deep hole boring: A stability analysis by Lie Li, Yuchen Ren, Zikai Shen, Junna Lu, Linhai Tong

“…In this study, a nonlinear model is developed to investigate the vibration stability of the boring process, with the model's dimensionless parameters analyzed and solved using the Runge-Kutta method. The impact of nonlinear parameters associated with the damping and stiffness of the absorbers on the vibration characteristics of boring bars is thoroughly examined. …”
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STUDY ON NONLINEAR DYNAMICS OF ASYMMETRICAL SUPPORTED ROTOR UNDER INFLUENCE OF HEELING ANGLE by LI Mo, LIU YongBao, WANG Qiang

“…The variable-step fourth-order Runge-Kutta method was used to solve the system’ s dynamic equations,and the nonlinear theory were used to analyze the simulation results. …”
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Wind Turbine Aerodynamic Performance by Lifting Line Method by Horia Dumitrescu, Vladimir Cardos

“…Performance parameters are calculated by application of the Biot-Savart law along with the Kutta-Joukowski theorem. Predictions are, shown to compare favorably with existing numerical data from more involved free wake methods, but require less computational effort. …”
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Deterministic Epidemic Models for Ebola Infection with Time-Dependent Controls by Eric Okyere, Johnson De-Graft Ankamah, Anthony Kodzo Hunkpe, Dorcas Mensah

“…The forward-backward sweep numerical scheme with the fourth-order Runge–Kutta method is used to solve the optimality system for the various control strategies. …”
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The Stochastic Resonance Phenomenon of Different Noises in Underdamped Bistable System by Shan Yang, Zening Fan, Ruibin Ren

“…Then, the factors of influence to the SR are investigated by the Euler-Maruyama algorithm, Milstein algorithm, and fourth-order Runge-Kutta algorithm, respectively. The results show that the SR phenomenon can be generated in the proposed system under certain conditions by adjusting the parameters of the control effect with different noises. …”
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Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral by Li Wen, Li Cui, Hairong Lin, Fei Yu

“…We apply the Gauss–Legendre integral and the Runge–Kutta algorithm to the solution of dissipative chaotic systems for the first time and analyze and compare the differences between the two algorithms. …”
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Implementation and Experiment of a Novel Molecular Spring Isolator by Gaofa Nie, Xuhong Miao, Yuhang Tang, Qian Chen

“…An averaging method is devoted to computing the primary resonance response and its accuracy is proved by the fourth-order Runge–Kutta method. Furthermore, the energy transmissibility is used to estimate its vibration isolation capability. …”
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Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms by A. H. Bhrawy, L. M. Assas, M. A. Alghamdi

“…In the second step, the implicit Runge-Kutta method of fourth order is applied to solve a system of ODEs of second order in time. …”
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Research of Dynamics Modeling Method for Rolling Bearing with Surface Damage Fault by Wu Jigang, Yang Zengzeng, Jiang Mian, Li Xuejun

“…The vibration models are solved with fourth- order Runge- Kutta method,and then the vibration data of inner ring are obtained and analyzed in frequency spectrum. …”
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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

“…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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The Dynamical Behavior of a Rigid Body Relative Equilibrium Position by T. S. Amer

“…The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. …”
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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

“…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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Estimation of aboveground biomass and carbon storage in mangroves along the coast of Banda Aceh City by Farahisah Harum, Nanda Muhammad, Haditiar Yudi, Khairunnisa

“…Data collection was conducted at four stations, namely Station 1 in Meuraxa District, Station 2 in Kuta Raja District, Station 3 in Kuta Alam District, and Station 4 in Syiah Kuala District, using a 100 m² quadrat transect method. …”
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Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation method by Tapas Roy, Aya Soqi, Dilip K. Maiti, Rania Wannan, Jihad Asad

“…Furthermore, the analytical expressions in series form, which is very close to the numerical solution of Runge-Kutta method is obtained. In addition, the analytical expression for the amplitude and the frequency of the oscillations for two cases: simple regular oscillation and the irregular oscillation is computed. …”
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Influence of Parameter on Dynamic Load and Load Sharing Characteristic of Split Torque-combine Power Gear Transmission System by He Lin, Sanmin Wang

“…By applying the fourth order Runge-Kutta algorithm to solve the system dimensionless dynamical equations， dynamic load characteristic is analyzed under the excitations of backlash， general transmission error and time-varying mesh stiffness. …”
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STUDY ON THE DYNAMIC CHARACTERISTICS OF A SYSTEM WITH A LOOSE-RUBBING COUPLED FAULTY ROTOR (MT) by FU YongBing

“…A dynamic model of rotor system with loosening and rubbing multiple faults coupling was established. Fourth-order Runge-Kutta method was used for numerical simulation. Periodic bifurcation diagram of rotor system, maximum rub-impact force diagram, amplitude diagram of loose bearing support, phase diagram as well as Poincaré map of the rotor system were obtained. …”
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MHD Heat and Mass Transfer of Chemical Reaction Fluid Flow over a Moving Vertical Plate in Presence of Heat Source with Convective Surface Boundary Condition by B. R. Rout, S. K. Parida, S. Panda

“…The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. …”
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