Solutions of the Force-Free Duffing-van der Pol Oscillator Equation by Najeeb Alam Khan, Muhammad Jamil, Syed Anwar Ali, Nadeem Alam Khan

“…The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. …”
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The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators by D. V. Hieu, N. Q. Hai, D. T. Hung

“…The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min–Max Approach (MMA), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Energy Balance Method (EBM), Harmonic Balance Method (HBM), 4th-Order Runge-Kutta Method, and the exact ones. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully applied to a lot of practical engineering and physical problems.…”
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Analysis of Nonlinear Dynamics Characteristic of Spur Gear Pair System with Fault by Wang Yongliang, Wan Yanjing, Yin Fengwei, Yang Liu

“…The nonlinear dynamics equations with faults are solved by employing 4~5 order variable step size Runge-Kutta method. The bifurcation diagrams， phase portraits and Poincaré maps of the single-stage gear system under the condition of no fault, mild wear fault and crack fault are obtained to research the nonlinear dynamics characteristic of system. …”
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KUZEY AFRİKA’DA YENİ İBÂDÎ ELYAZMALARI by Harun Yıldız, Amr Halîfe En-nâmî

“…ELUNDo \]\ÈOGD EX OLWHUDWUGHQ ID\GDODQPD LPNDQÈ EXODPDPÈëWÈU 6kOLPvªQLQ V|\OHGLèL JLEL §]DPDQÈQ WDKULEDWÈ RQODUÈQ oRèXQX \DNDODPÈëWÈU¨ 2 0VOPDQ ODU DUDVÈQGDNL VDYDëODUGD PXKDOLIOHULQ OLWHUDWUQ WDKULS HWPHN \D\JÈQ ELU X\JXODPD ROPXëWX EX QHGHQOH éEkGvOHU 7kKHUWªWHNL HO 0DªVPH LOH &HEHO L 1HIVHªGHNL .DVU 9HOkP NWSKDQHOHULQGH EXOXQDQ HVHUOHULQL ND\EHWPLëOHU GLU…”
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An Accurate Predictor-Corrector-Type Nonstandard Finite Difference Scheme for an SEIR Epidemic Model by Asma Farooqi, Riaz Ahmad, Rashada Farooqi, Sayer O. Alharbi, Dumitru Baleanu, Muhammad Rafiq, Ilyas Khan, M. O. Ahmad

“…Simulations are performed to guarantee the results, and its effectiveness is compared with well-known numerical methods such as Runge–Kutta (RK) and Euler method of a predictor-corrector type.…”
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Approximate Solutions of Fisher's Type Equations with Variable Coefficients by A. H. Bhrawy, M. A. Alghamdi

“…The four-stage A-stable implicit Runge-Kutta scheme is applied to solve the resulted system of first order in time. …”
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Study on Dynamics of Planetary Gear Transmission Considering Backlash by Da Min, Guangming Zou, Xingdong Wang, Wei Tang

“…Four influences factors，namely backlash，time-varying meshing stiffness，meshing damping and comprehensive meshing error，are considered in the model，the dynamics equations corresponding to the model are listed and solved by the fourth-order Runge Kutta method. By changing the size of the backlash，the response states of the system under different backlash sizes are obtained. …”
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An FFT-Based Spectral Analysis Method for Linear Discrete Dynamic Systems with Non-Proportional Damping by Jooyong Cho, Usik Lee

“…The accuracy of the proposed FFT-based spectral analysis method is evaluated by comparing the forced vibration responses obtained by the present FFT-based spectral analysis method with those obtained by using the well-known Runge-Kutta method and modal analysis method.…”
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Soret and Dufour Effects on Natural Convection Flow Past a Vertical Surface in a Porous Medium with Variable Viscosity by M. B. K. Moorthy, K. Senthilvadivu

“…The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge-Kutta-Gill method along with shooting technique. …”
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Dufour and Soret Effects on Melting from a Vertical Plate Embedded in Saturated Porous Media by Basant K. Jha, Umaru Mohammed, Abiodun O. Ajibade

“…The resulting system of nonlinear ordinary differential equations is solved numerically using Runge Kutta-Fehlberg with shooting techniques. Numerical results are obtained for the velocity, temperature, and concentration distributions, as well as the Nusselt number and Sherwood number for several values of the parameters, namely, the buoyancy parameter, melting parameter, Dufour effect, Soret effect, and Lewis number. …”
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Quality Assessment Method for Chromite Sand to Reduce the Number of Cast Steel Surface Defects by T. Wróbel, J. Jezierski, D. Bartocha, E. Feliks, A. Paleń

“…Moreover, clear suggestions were developed concerning the ability to use the given chromite sand batch as the base of moulding sand made in Alphaset technology in Huta Małapanew Sp. z o.o.…”
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DYNAMIC CHARACTERISTICS ANALYSIS OF FLEXIBLE FOUNDATION VIBRATION ISOLATION SYSTEM by ZHANG DaoKun, HUO Rui, LI ShuYing, WANG ZhiDong

“…Based on an example of vibration isolation system of a small unmanned aircraft engine,the Runge-Kutta method is applied to simulation and estimation of power flow transmitted through nonlinear isolators with hypothetical different stiffness characteristics. …”
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Variational Iteration Method of Dropping Shock Response for the Suspension Spring Packaging System by Shuang Song, An-Jun Chen

“…The nondimensional peak of displacement, the nondimensional peak of acceleration, and the dropping shock extended period were compared with the results of the Runge-Kutta method, at which relative errors were less than 4%. …”
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Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid by Norihan Md. Arifin, Roslinda Nazar, Ioan Pop

“…Numerical solutions of the similarity equations are obtained using the Runge-Kutta-Fehlberg (RKF) method. Three different types of nanoparticles are considered, namely, Cu, Al2O3, and TiO2, by using water as a base fluid with Prandtl number Pr=6.2. …”
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Investigation of a spatial double pendulum: an engineering approach by S. Bendersky, B. Sandler

“…Matlab computer programs were used for solving the nonlinear differential equations by the Runge-Kutta method. Fourier transformation was used to obtain the frequency spectra for analyses of the oscillations of the two pendulums. …”
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Numerical Approximation for Fractional Neutron Transport Equation by Zhengang Zhao, Yunying Zheng

“…In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. …”
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An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation by Chaeyoung Lee, Jintae Park, Soobin Kwak, Sangkwon Kim, Yongho Choi, Seokjun Ham, Junseok Kim

“…The proposed adaptive time-stepping algorithm is based on the Runge–Kutta–Fehlberg method, where the local truncation error is estimated by using fourth- and fifth-order numerical schemes. …”
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Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling by O. D. Makinde, S. Khamis, M. S. Tshehla, O. Franks

“…These equations are solved analytically by regular perturbation methods with series improvement technique and numerically using an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. …”
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Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption by Khilap Singh, Manoj Kumar

“…The dimensionless governing equations for this investigation are solved by Runge-Kutta-Fehlberg fourth fifth-order method with shooting technique. …”
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Modeling and Dynamics Characteristic Analysis of Helical Gear System with Considering Tooth Surface Friction by Kang Boqiang, Gou Xiangfeng

“…The movement differential equations are discussed by the variable step size Runge- Kutta method. The bifurcation diagrams,Lyapunov exponents,cloud pictures of the maximum amplitude and the amplitude- frequency characteristic superposition graphs are obtained and the system dynamics characteristic variation with frequency is analyzed. …”
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