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fourth-order runge–kutta method (matlab ode45)  (MathWorks Inc)


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    MathWorks Inc fourth-order runge–kutta method (matlab ode45)
    Fourth Order Runge–Kutta Method (Matlab Ode45), supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/fourth-order+runge%E2%80%93kutta+method+(matlab+ode45)/pm40403759-35-215-218
    Average 90 stars, based on 1 article reviews
    fourth-order runge–kutta method (matlab ode45) - by Bioz Stars, 2026-09
    90/100 stars

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    Article Title: Phase transitions in 2D multistable mechanical metamaterials via collisions of soliton-like pulses
    Article Snippet: Then, full-scale simulations can be conducted by numerically solving the system’s EOMs using the fourth order Runge-Kutta method (via the Matlab function ode45).

    Article Title: Relative density and isobaric expansivity of cold and supercooled heavy water from 254 to 298 K and up to 100 MPa.
    Article Snippet: A dual-capillary apparatus was developed for highly accurate measurements of density of liquids, including the supercooled liquid region.. The device was used to determine the density of supercooled heavy water in the temperature range from 254 K to 298 K at pressures ranging from atmospheric to 100 MPa, relative to density at reference isotherm 298.15 K. The measurements of relative density were reproducible within 10 ppm, and their expanded (k = 2) uncertainty was within 50 ppm.. To obtain absolute values of density, thermodynamic integration was performed using recent accurate speed of sound measurements in the stable liquid region.

    Article Title: Numerical investigation on the influence of dual-frequency coupling parameters on acoustic cavitation and its analysis of the enhancement and attenuation effect.
    Article Snippet: Therefore, the fourth-order Runge Kutta method (the corresponding Matlab function is ode45) is adopted to obtain the numerical solution by reducing the order of the above equation.

    Article Title: Dynamics and design of passive tails for enhanced stability of motion.
    Article Snippet: ∆l1 = [ un+1 − un − Ln+12 cos ( θn+1 + θ 0 n+1 ) − Ln2 cos ( θn + θ 0 n ) + Ln+12 cos ( θ0n+1 ) + Ln2 cos ( θ0n ) vn+1 − vn + Ln+12 sin ( θn+1 + θ 0 n+1 ) + Ln2 sin ( θn + θ 0 n ) − Ln+12 sin ( θ0n+1 ) − Ln2 sin ( θ0n ) ] (3) ∆l2 = [ un − un−1 − Ln2 cos ( θn + θ 0 n ) − Ln−12 cos ( θn−1 + θ 0 n−1 ) + Ln2 cos ( θ0n ) + Ln−12 cos ( θ0n−1 ) vn − vn−1 + Ln2 sin ( θn + θ 0 n ) + Ln−12 sin ( θn−1 + θ 0 n−1 ) − Ln2 sin ( θ0n ) − Ln−12 sin ( θ0n−1 ) ] (4) ∆θ1 = θn+1 + θn + θ 0 n+1 + θ 0 n − θLinn+1 − θLinn (5) ∆θ2 = θn + θn−1 + θ 0 n + θ 0 n−1 − θLinn − θLinn−1. (6) From equations (1) and (2), we have derived the equations of motion for the nth unit (see note 4 in the supplemental material [44] for details) and use the fourth-order Runge–Kutta method (Matlab ode45) to simulate the system’s response when subjected to impulsive loading (prescribed as a displacement and velocity profile in the simulations).

    Article Title: Dimensionless Framework for Seed Recipe Design and Optimal Control of Batch Crystallization
    Article Snippet: In order to study and propose guidelines for the design and control of batch crystallization systems with different growth and nucleation parameters, optimal control theory and a dimensionless batch crystallization model are applied to solve multi-objective optimization problems in a nearly analytical and computationally efficient way.. Optimal growth rate trajectories and the corresponding critical seed recipes (seed loading ratio and seed mean size that make nucleated mass negligible) representing a suitable trade-off between two objective functions (number of nuclei and nucleated mass) are derived for 32 chemical systems.. The results are also compared with results from applying supersaturation control, a strategy that can be implemented without a kinetic model.

    Article Title: Accuracy of a one-dimensional reduction of dynamical systems on networks
    Article Snippet: We calculate x∗eff by running Eq. (1) using the fourth-order Runge-Kutta method (with MATLAB function ode45) until it converges and substituting the final values of xi (with i = 1, . . . , N), which we denote by x∗i , into Eq. (9).

    Article Title: Removal of aqueous Cr(VI) by a magnetic biochar derived from Melia azedarach wood.
    Article Snippet: Magnetic biochar (MMABC) prepared from Melia azedarach wood was used for aqueous Cr(VI) removal.. MMABC was a mesoporous material with SBET 5.219m/g and superparamagnetic magnetization 17.3 emu/g contributed by the contained Fe3O4.. The MMABC showed higher removal efficiency (99.8%) than biochar under conditions of dosage 5 g/L, pH=3.0, and Cr(VI) concentration 10mg/L.

    Article Title: Emergent subharmonic band gaps in nonlinear locally resonant metamaterials induced by autoparametric resonance
    Article Snippet: The ordinary differential equations (1) describing the momentum balance of this system are integrated numerically using an explicit time integration method, i.e., the fourth-order Runge-Kutta method (ODE45, MATLAB).



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