Search Results - Runge-Kutta numerical integration algorithm

Explicit pseudo two-step exponential Runge–Kutta methods for the numerical integration of first-order differential equations by Fang, Yonglei, Hu, Xianfa, Li, Jiyong

“…This paper is devoted to the explicit pseudo two-step exponential Runge–Kutta (EPTSERK) methods for the numerical integration of first-order ordinary differential equations…”
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Parameter estimation and modeling of nonlinear dynamical systems based on Runge–Kutta physics-informed neural network by Zhai, Weida, Tao, Dongwang, Bao, Yuequan

“… estimation and modeling based on the combination of the physics-informed neural network (PINN) and Runge–Kutta algorithm. Drawing inspiration from classical numerical…”
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The generalization of diagonally implicit Runge–Kutta–Nyström method with controllable numerical dissipation for structural dynamics by Wang, Yazhou, Xue, Xiaodai, Wang, Tao, Xie, Ningning, Jia, Hongjin, Hu, Zhubing, Tamma, Kumar

“… The significant advances and contributions are summarized as follows: (1) the identity between the composite time-integration algorithms and the diagonally implicit Runge…”
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Validated computation of the local truncation error of Runge-Kutta methods with automatic differentiation by Mullier, Olivier, Chapoutot, Alexandre, Alexandre dit Sandretto, Julien

“… In particular, this specialized algorithm is combined with set-membership framework to define validated numerical integration methods based on Runge-Kutta methods…”
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Derivation of three-derivative Runge-Kutta methods by Turacı, Mukaddes Ökten, Öziş, Turgut

“…We introduce an algorithm for a numerical integration of ordinary differential equations in the form of y ′ = f ( y…”
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Nonlinear forced vibrations of supported pipe conveying fluid subjected to an axial base excitation by Zhou, K., Ni, Q., Dai, H.L., Wang, L.

“… The resulting equations are then solved by a fourth-order Runge-Kutta integration algorithm. Numerical results indicate that the excitation amplitude and internal flow velocity have a combined effect on the dynamic responses of the pipe…”
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Numerically efficient modified Runge–Kutta solver for fatigue crack growth analysis by Amann, Christian, Kadau, Kai

“… We present a modified Runge–Kutta algorithm which yields a conservative estimate of the crack size for fatigue crack growth even for large integration step sizes…”
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Runge–Kutta–Nyström methods adapted to the numerical integration of perturbed oscillators by Franco, J.M.

“…New Runge–Kutta–Nyström methods specially adapted to the numerical integration of perturbed oscillators are obtained…”
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Vibration and stability of an axially moving Rayleigh beam by Chang, Jer-Rong, Lin, Wei-Jr, Huang, Chun-Jung, Choi, Siu-Tong

“… The vibration and stability of beams with these motions are investigated. For vibration analysis, direct time numerical integration, based on a Runge…”
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Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations by Ju, Lili, Li, Xiao, Qiao, Zhonghua, Yang, Jiang

“… Investigation on numerical algorithms with preservation of the MBP has attracted increasingly attentions in recent years, especially for the temporal discretizations, since the violation of MBP…”
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Application of the Bezier integration technique with enhanced stability in forward dynamics of constrained multibody systems with Baumgarte stabilization method by Khoshnazar, Mohammad, Dastranj, Mohammad, Azimi, Ali, Aghdam, Mohammad M., Flores, Paulo

“… It is well known that constraints violation and instability are amongst the main computational difficulties of various numerical integration algorithms to provide accurate solutions for DAEs…”
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Gyrotactic microbes' movement in a magneto-nano-polymer induced by a stretchable cylindrical surface set in a DF porous medium subject to non-linear radiation and Arrhenius kinetics by Sarkar, Soumitra, Das, Sanatan

“…Because of its numerous uses in biotechnology, bioengineering, biosensors, and bioinformatics, bioconvection involving microbes and nanoparticles has attracted…”
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Application of Runge–Kutta–Merson algorithm for creep damage analysis by Ling, Xiang, Tu, Shan-Tung, Gong, Jian-Ming

“…A Runge–Kutta–Merson (RKM) numerical integration algorithm for creep damage analysis is presented in this paper…”
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Relaxation Runge–Kutta Methods for Hamiltonian Problems by Ranocha, Hendrik, Ketcheson, David I.

“…The recently-introduced relaxation approach for Runge–Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems…”
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Dynamic modeling and analysis for transmission system of high-power wind turbine gearbox by Zhai, Hongfei, Zhu, Caichao, Song, Chaosheng, Liu, Huaiju, Li, Guangfu, Ma, Fei

“… Numerical integration applying the explicit 4/5th order Runge-Kutta algorithm was used to solve the proposed model and the dynamic responses of transmission system were investigated…”
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In situ hydrolysis of epoxidized oleic acid by catalytic epoxidation-peracids mechanism by Jalil, Mohd Jumain, Azmi, Intan Suhada, Hadi, Abdul, Yamin, Aliff Farhan Mohd

“… is simpler and high relative conversion to oxirane (85.7%). Then, a mathematical model was developed by using the numerical integration Runge Kutta 4 th Order method…”
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Relativistic resistive magneto-hydrodynamics code for high-energy heavy-ion collisions by Nakamura, Kouki, Miyoshi, Takahiro, Nonaka, Chiho, Takahashi, Hiroyuki R.

“… For the non-stiff part, we evaluate the numerical flux using HLL approximated Riemann solver and execute the time integration by the second-order of Runge–Kutta algorithm…”
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Novel Consistent Tangent Operator for Runge–Kutta‐Based Explicit Stress Integration for Elasto‐Plastic Models: Application to the Modified Cam Clay Model by Monforte, L., Rouainia, M.

“…–Raphson algorithm used in solving the global problem. Therefore, when employing explicit stress integration, the typical convergence rate of the global problem is linear…”
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Dynamic analysis of a flexible rotor supported by ball bearings with damping rings based on FEM and lumped mass theory by Zhu, Hai-min, Chen, Wei-fang, Zhu, Ru-peng, Zhang, Li, Gao, Jie, Liao, Mei-jun

“… The governing equations were solved by precise integration and the Runge-Kutta hybrid numerical algorithm…”
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Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity by Avitabile, Daniele, Bridges, Thomas J.

“… For the numerical integration, Gauss–Legendre Runge–Kutta algorithms are the principal choice for preserving orthogonality, and performance results are shown for a range of GLRK methods. The theory and methods are tested by application to example boundary value problems including the Orr–Sommerfeld equation in hydrodynamic stability…”
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