Vortex-Induced Vibration of a Cable-Stayed Bridge by M. T. Song, D. Q. Cao, W. D. Zhu

“…Orthogonality conditions of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert coupled governing partial differential equations of the original cable-stayed bridge model with damping to a set of ordinary differential equations by using Galerkin method. …”
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New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity by Wedad Saleh, Hamid Boulares, Abdelkader Moumen, Hussien Albala, Badreddine Meftah

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Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. by Byonaneebye, Darius

“…The Dormand-Prince method is a technique similar to the Runge-Kutta method for solving ordinary differential equations (ODEs). It uses six function evaluations to compute solutions with fourth and fifth-order accuracy. …”
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Existence of Positive Solutions for a Functional Fractional Boundary Value Problem by Chuanzhi Bai

“…We study the existence of positive solutions for a boundary value problem of fractional-order functional differential equations. Several new existence results are obtained.…”
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Notes on almost-periodicity in topological vector spaces by Gaston Mandata N'guérékata

“…A study is made of almost-periodic functions in topological vector spaces with applications to abstract differential equations.…”
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Application of artificial intelligence brain structure-based paradigm to predict the slip condition impact on magnetized thermal Casson viscoplastic fluid model under combined temp... by Umar Farooq, Shan Ali Khan, Haihu Liu, Muhammad Imran, Lotfi Ben Said, Aleena Ramzan, Taseer Muhammad

“…With the help of a similarity transformation, the complex partial differential equations governing the flow and energy take on the form of nonlinear ordinary differential equations. …”
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The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion by Zulqurnain Sabir, Assad Ayub, Juan L. G. Guirao, Saira Bhatti, Syed Zahir Hussain Shah

“…The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. …”
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Numerical Solution of Binary Liquid-Phase Adsorption onto Porocel Clay Using Linear, Freundlich and Langmuir Isotherms by Olaosebikan A. Olafadehan, Alfred A. Susu

“…The scheme is based on orthogonal collocation for spatial discretization of the resulting set of coupled hyperbolic and parabolic partial differential equations for the macro-and micro-system, respectively. …”
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Computational analysis of EMHD nanofluid flow over a thermally conductive surface: Enhancing heat transfer for industrial applications by Faiza Zahid, Muhammad Bilal Riaz

“…The problem under scrutiny yields a non-similar solution necessitating the transformation of governing partial differential equations into ordinary differential equations by the use of similarity variables. …”
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Mathematical modeling of velocity and accelerations fields of image motion in the optical equipment of the Earth remote sensing satellite by S. Yu. Gorchakov

“…For modeling the orbital and angular motion of the satellite, differential equations with numerical integration were used. …”
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Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn by Muhammad Shakeel, Naseem Abbas, Muhammad Junaid U. Rehman, Fehaid Salem Alshammari, Abdullah Al-Yaari

“…Using a transformation method, the nonlinear partial differential equations (NPDEs) are converted into various nonlinear ordinary differential equations (NLODEs), providing the numerous closed-form solitary wave solutions. …”
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Analytical Investigation of Laminar Viscoelastic Fluid Flow over a Wedge in the Presence of Buoyancy Force Effects by B. Rostami, M. M. Rashidi, P. Rostami, E. Momoniat, N. Freidoonimehr

“…The two-dimensional boundary-layer governing partial differential equations (PDEs) are derived by the consideration of Boussinesq approximation. …”
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Nonlinear Vibration Analysis for Stiffened Cylindrical Shells Subjected to Electromagnetic Environment by Xue-Qin Li, Guang-Chen Bai, Lu-Kai Song, Wei Zhang

“…By employing the Galerkin discretization procedure, the partial differential equations are diverted to a set of coupled nonlinear ordinary differential equations of motion. …”
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Nonlinear Dynamic Behavior of Winding Hoisting Rope under Head Sheave Axial Wobbles by Guoying Wang, Xingming Xiao, Chi Ma, Gang Cheng, Xiao Di

“…The governing equations are nonlinear infinite-dimensional partial differential equations, which are discretized into the finite-dimensional ordinary differential equations through the Galerkin method. …”
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Analysis of the Physical Behavior of the Periodic Mixed-Convection Flow around a Nonconducting Horizontal Circular Cylinder Embedded in a Porous Medium by Muhammad Ashraf, Zia Ullah, Saqib Zia, Sayer O. Alharbi, Dumitru Baleanu, Ilyas Khan

“…For this purpose, a model in the form of partial differential equations is formulated, and then, the governing equations of the dimensionless model are transformed into the primitive form for integration by using primitive variable formulation. …”
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Theoretical and numerical study of profit in agricultural sector model using wavelet method by Yeshwanth R., Kumbinarasaiah S.

“…The operational matrices are used to simplify fractional differential equations to an algebraic system of equations. …”
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Irreversibility and Sensitivity analysis of MHD squeezing various shaped nanofluid flow between parallel permeable disks by Abdul Awal, Md. Sarwar Alam

“…The system of partial differential equations governing the flow is converted to a coupled of non-dimension ordinary differential equations. …”
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Analysis of the Three-Dimensional Dynamic Problems by Using a New Numerical Method by Yao Rong, Yang Sun, LiQing Zhu, Xiao Xiao

“…In this paper, the scaled boundary element method (SBFEM) is used to analyze the displacement and pore pressure response of saturated soil due to consolidation under dynamic load. The partial differential equations of linear problems are transformed into ordinary differential equations and solved along the radial direction. …”
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Some Relations between Certain Complex Equations and Nonnormalized Meromorphic Functions by Hüseyin Irmak

“…The purpose of this investigation is first to reveal some relations between certain complex (differential) equations and nonnormalized meromorphic functions and then to point some of their useful consequences out.…”
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S-asymptotic expansion of distributions by Bogoljub Stankovic

“…This paper contains first a definition of the asymptotic expansion at infinity of distributions belonging to G′Rn, named S-asymptotic expansion, as also its properties and application to partial differential equations.…”
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