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  1. 1841

    Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink by I. Swain, S. R. Mishra, H. B. Pattanayak

    Published 2015-01-01
    “…The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. Graphical results are displayed for nondimensional velocity, temperature, and concentration profiles while numerical values of the skin friction local Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system.…”
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    Article
  2. 1842

    Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays by Adsadang Himakalasa, Suttida Wongkaew

    Published 2021-01-01
    “…Moreover, the existence of the first-order optimality conditions for a delayed optimal control problem is discussed. Furthermore, the Runge–Kutta discretization method and the nonlinear conjugate gradient method are employed to solve the discrete optimality system. …”
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  3. 1843

    The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System by M. S. H. Chowdhury, Nur Isnida Razali, Waqar Asrar, M. M. Rahman

    Published 2015-01-01
    “…To ensure the precision of the technique applied in this work, the results are compared with a fourth-order Runge-Kutta method and the standard HPM. The results show that the MHPM is an efficient and powerful technique in solving both chaotic and hyperchaotic systems.…”
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  4. 1844

    Solving Hyperchaotic Systems Using the Spectral Relaxation Method by S. S. Motsa, P. G. Dlamini, M. Khumalo

    Published 2012-01-01
    “…To demonstrate the performance of the method, results are presented in tables and diagrams and compared to results obtained using a Runge-Kutta-(4,5)-based MATLAB solver, ode45, and other previously published results.…”
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  5. 1845

    Approximate Prediction-Based Control Method for Nonlinear Oscillatory Systems with Applications to Chaotic Systems by Thiago P. Chagas, Pierre-Alexandre Bliman, Karl H. Kienitz

    Published 2018-01-01
    “…The method is based on estimating future states of the free system response of continuous-time systems using the solution from the Runge-Kutta implicit method in real time. Some aspects of aPBC are evaluated in the present work, particularly its robustness to low future states estimation precision is exemplified.…”
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  6. 1846

    Investigation of a spatial double pendulum: an engineering approach by S. Bendersky, B. Sandler

    Published 2006-01-01
    “…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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  20. 1860