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  11. 1831

    Vom Einfall zum Gedanken. Arnold Schönbergs Tonalitätsdenken und dessen Entwicklung seit der Harmonielehre by Gerhard Luchterhandt

    Published 2012-01-01
    “…Der Konservativismus der späten amerikanischen Lehrwerke lässt sich allerdings wohl nur teilweise auf diesen Perspektivwechsel zurückführen – er dürfte eher pragmatische Gründe gehabt haben. Schönbergs partielle Rückkehr zu einer mutig experimentierenden tonalen Schreibweise (op. 38–40) Ende der 1930er Jahre zeigt nämlich, dass seine ursprüngliche Haltung zur Tonalität zumindest kompositorisch noch präsent war.…”
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  12. 1832

    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

    Published 2022-01-01
    “…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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  13. 1833

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

    Published 2011-01-01
    “…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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  14. 1834

    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

    Published 2012-01-01
    “…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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  15. 1835

    Reducing the Possibility of Ruin by Maximizing the Survival Function for the Insurance Company’s Portfolio by Masoud Komunte, Christian Kasumo, Verdiana Grace Masanja

    Published 2022-01-01
    “…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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  16. 1836

    Dynamic Effective Properties of Lead-Reinforced Epoxy Resin Composites with Differential Method by Haitao Zhu, Yongping Wan

    Published 2022-01-01
    “…The corresponding differential equations are numerically solved by the fourth-order Runge–Kutta method, and the dynamic effective modulus and density are obtained. …”
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  17. 1837

    Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method by M.R. Alharthi, Alvaro H. Salas, Wedad Albalawi, S.A. El-Tantawy

    Published 2022-01-01
    “…Moreover, the analytical approximation and numerical approximation using the Chebyshev collocation numerical method and the MATHEMATICA command Fit are compared with the Runge–Kutta (RK) numerical solution. Also, the maximum distance error to all obtained approximations is estimated with respect to the RK numerical solution. …”
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  18. 1838

    A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems by A. Karimi Dizicheh, F. Ismail, M. Tavassoli Kajani, Mohammad Maleki

    Published 2013-01-01
    “…The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.…”
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  19. 1839

    The Motion of a Rigid Body with Irrational Natural Frequency by A. I. Ismail

    Published 2020-01-01
    “…Using the digital fourth-order Runge-Kutta method, we determine the digital solutions of the obtained system. …”
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  20. 1840

    Dufour and Soret Effects on Melting from a Vertical Plate Embedded in Saturated Porous Media by Basant K. Jha, Umaru Mohammed, Abiodun O. Ajibade

    Published 2013-01-01
    “…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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