Adjustment of Optimal Parameters to Control the Temperature in Different Conductors by Amirhossein Oudi, Samaneh Faramarzi, Maryam Hosseini, Yegane Davoodbeygi

“…In this method, the differential equations expressing the process were written as simultaneous first order differential equations. …”
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A Fractional Epidemiological Model for Bone Remodeling Process by Muath Awadalla, Yves Yannick Yameni Noupoue, Kinda Abuasbeh

“…We finally obtained that modeling bone formation process using fractional differential equations yielded comparable results with those obtained through a system of classical differential equations. …”
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A New Numerical Approach for the Laminar Boundary Layer Flow and Heat Transfer along a Stretching Cylinder Embedded in a Porous Medium with Variable Thermal Conductivity by S. Shateyi, G. T. Marewo

“…A suitable similarity transformation is employed to transform the partial differential equations corresponding to the momentum and heat equations into nonlinear ordinary differential equations. …”
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Matrix Laplace Transform Method and It Applications on Spring-Mass Systems by Syamsul Arifin

“…There are several methods to solve an initial value problem of second-order homogenous linear systems of differential equations with constant coefficients. That are elimination method and matrix method. …”
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Modelling of vehicle motion control by Narimantas Listopadskis

“…Motion of the vehicle is determined by system of differential equ­ations. Fourth-order Runge–Kutta adaptive method was used for solving of the obtained system of the differential equations. …”
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Modelling of vehicle motion by Narimantas Listopadskis

“…Motion of the vehicle is determined by system of differential equations. Fourth-order Runge-Kutta adaptive method was used for solving of the obtained systems of the differential equations. …”
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Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow by H. Alighanbari, S. M. Hashemi

“…The aeroelastic integro-differential equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary differential equations. …”
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Research of Nonlinear Dynamic Characteristic of the Roller Movable Tooth Drive by Wang Zhigang, Pu Yunguo

“…The system nonlinear dynamics differential equations and coordinate transformation of differential equations are worked,and the non-dimensional treatment is carried out. …”
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Weighted Stepanov-Like Pseudoperiodicity and Applications by Zhinan Xia

“…Furthermore, the existence and uniqueness of the weighted pseudoperiodic solution to fractional integro-differential equations and nonautonomous differential equations are investigated. …”
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On Random Dynamical Systems Generated by White Noise Time Change of Deterministic Dynamical Systems by Mohamed Hmissi, Farida Mokchaha

“…We prove that the obtained random dynamical systems are solutions of some stochastic differential equations whenever the deterministic dynamical systems are solutions of ordinary differential equations.…”
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Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients by Peng Jiang, Xiaofeng Ju, Dan Liu, Shaoqun Fan

“…The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. …”
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Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes by Matteo Strozzi, Francesco Pellicano

“…The Rayleigh–Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. …”
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Similarity Solutions for Flow and Heat Transfer of Non-Newtonian Fluid over a Stretching Surface by Atta Sojoudi, Ali Mazloomi, Suvash C. Saha, Y. T. Gu

“…The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. …”
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Integral Representation of Functions of Bounded Variation by Z. Lipcsey, I. M. Esuabana, J. A. Ugboh, I. O. Isaac

“…With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations. …”
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A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators by Yassin Belkourchia, Lahcen Azrar

“…Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. …”
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Significance of Marangoni convection in ethylene glycol base hybrid nanofluid flow with viscous dissipation through a porous medium by Ali Rehman, Ilyas Khan, Sultan Alshehery, Muhammad Sabaoon Khan

“…The authors applied appropriate transformations to convert a collection of dimension form of nonlinear partial differential equations to dimensionless form of nonlinear ordinary differential equations. …”
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Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry by K. S. Mahomed, E. Momoniat

“…By use of the Lie symmetry group methods we analyze the relationship between the first integrals of the simplest linear third-order ordinary differential equations (ODEs) and their point symmetries. …”
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Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries by Bermúdez, Alfredo, Padín, Iago

“…For this purpose, advantage is taken from the fact that optimal control problems for stochastic ordinary differential equations (SDE) can be equivalently formulated as optimal control problems for deterministic partial differential equations (PDE), namely, the corresponding Fokker–Planck equation.…”
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Lie and Riccati Linearization of a Class of Liénard Type Equations by A. G. Johnpillai, C. M. Khalique, F. M. Mahomed

“…The linearizing transformations are used to transform the underlying class of equations to linear third- and second-order ordinary differential equations, respectively. The general solution of this class of equations can then easily be obtained by integrating the linearized equations resulting from both of the linearization approaches. …”
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A new finite difference algorithm for boundary value problems involving transmission conditions by Semih Çavuşoğlu, Oktay Sh. Mukhtarov

“…The finite difference method (FDM) is used to find an approximate solution to ordinary and partial differential equations of various type using finite difference equations to approximate derivatives. …”
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