Nonlocal Nonlinear Optical Response of Ionic Liquids under Violet Excitation by Cássio E. A. Santos, Márcio A. R. C. Alencar, Pedro Migowski, Jairton Dupont, Jandir M. Hickmann

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Analysis of Factors Affecting Road Transport Accidents of Hazardous Materials Based on PG-BN by Zewen Li, Mengmeng Zhang

“…However, considering the possible overfitting phenomenon of the BN model, the model was optimised by combining Pearson’s chi-squared test and Granger causality test (PG) methods. First, the data of hazardous materials accidents were preprocessed, and the index system of factors affecting hazardous materials road transport was constructed from five dimensions of “people, vehicles, hazmat, roads, and environment”; second, Pearson’s chi-squared test and the Granger causality test were used to screen the factors affecting hazardous materials road transport accidents and to determine the causal relationship between the factors; finally, the BN model was constructed with accident severity and accident processing time as target nodes, and the results were analyzed and validated. …”
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A Política Educacional ‘São Paulo Faz Escola’ na Educação do Campo by Mariana Padovan Farah Soares, Érika Porceli Alaniz, Marcos Vinicius Francisco

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Bilinguismo, biliteracia e alfabetização bilíngue by Ingrid Finger

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Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems by Hassan Saberi Nik, Paulo Rebelo

“…We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.…”
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Free convective flow of a stratified fluid through a porous medium bounded by a vertical plane by H. K. Mondal, T. K. Chaudhury

“…Velocity distribution is also obtained for certain values of the parameters by integrating the coupled differential equations by Runge-Kutta method and compared with the analytical solution. …”
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Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates by Saeed Dinarvand, Abed Moradi

“…The validity of our solutions is verified by the numerical results obtained by shooting method, coupled with Runge-Kutta scheme.…”
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On a New Reliable Algorithm by A. K. Alomari, M. S. M. Noorani, R. Nazar

“…Comparisons between the MSHAM solutions and the fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear systems of ordinary differential equations.…”
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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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A Numerical Comparison for a Discrete HIV Infection of CD4+ T-Cell Model Derived from Nonstandard Numerical Scheme by Mevlüde Yakıt Ongun, İlkem Turhan

“…This proposed nonstandard numerical scheme is compared with the classical explicit Euler and fourth order Runge-Kutta methods. To show the efficiency of this numerical scheme, the simulated results are given in tables and figures.…”
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Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting by Karima Mokni, Mohamed Ch-Chaoui

“…The model is formulated in terms of difference equations and derived by using the higher-order implicit Runge Kutta method with a very small step size to attain a discrete time version of its continuous counterpart. …”
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The Coupled Nonlinear Schrödinger Equations Describing Power and Phase for Modeling Phase-Sensitive Parametric Amplification in Silicon Waveguides by Xuefeng Li, Zhaolu Wang, Hongjun Liu

“…Through solving the coupled NLS equations by the split-step Fourier and Runge-Kutta integration methods, the numerical results show that the coupled NLS equations can perfectly describe and character the PS amplification process in silicon waveguides.…”
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Study of Polarized Wave with a Hydrodynamic Model and Fourier Spectral Method by Dennis Ling Chuan Ching, Zainal Abdul Aziz, Faisal Salah

“…The model is then solved by Fourier spectral and Runge-Kutta 4 methods, and the surface plot is drawn. …”
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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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Recoil and Vibration in an Archery Bow Equipped with a Multi-Rod Stabilizer by Igor Zaniewski

“…The research methods are based on the Euler-Bernoulli theory of beam bending, Lagrange equations of the second kind, the Cauchy problem, and the Runge-Kutta method. A mathematical software package was used to analyze the problem. …”
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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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Commutants of the Pommiez operator by Ivan H. Dimovski, Valentin Z. Hristov

“…The Pommiez operator (Δf)(z)=(f(z)−f(0))/z is considered in the space ℋ(G) of the holomorphic functions in an arbitrary finite Runge domain G. A new proof of a representation formula of Linchuk of the commutant of Δ in ℋ(G) is given. …”
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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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A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation by Liquan Mei, Yali Gao, Zhangxin Chen

“…A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. …”
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On the Approximate Analytical Solution to Non-Linear Oscillation Systems by Mahmoud Bayat, Iman Pakar

“…In the end, numerical comparisons are conducted between the results obtained by the Variational Approach and numerical solution using Runge-Kutta's [RK] algorithm to illustrate the effectiveness and convenience of the proposed methods.…”
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