Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations by Shaobo Zhou

“…We will prove that the Euler-Maruyama (EM) method can preserve almost surely exponential stability of stochastic pantograph differential equations under the linear growth conditions. …”
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Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms by A. H. Bhrawy, L. M. Assas, M. A. Alghamdi

“…Since the collocation method approximates ordinary differential equations, partial differential equations, and integral equations in physical space, it is very easy to implement and adapt to various problems, including variable coefficient and nonlinear differential equations. …”
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Novel Analysis of Fuzzy Fractional Emden-Fowler Equations within New Iterative Transform Method by M. Mossa Al-Sawalha, Naila Amir, Rasool Shah, Muhammad Yar

“…The analytical behavior of fractional differential equations is often puzzling and difficult to predict under uncertainty. …”
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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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Holomorphic embedding method for large-scale reverse osmosis desalination optimization by Junzhi Chen, Tao Wang, Jiu Luo, Hongbo Chen, Yi Heng

“…Abstract Large-scale optimal design problems involving nonlinear differential equations are widely applied in modeling such as craft manufacturing, chemical engineering and energy engineering. …”
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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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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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Global Stability for Fractional Diffusion Equations in Biological Systems by Khalid Hattaf, Noura Yousfi

“…This paper proposes a new method of construction of Lyapunov functionals for the dynamical systems described by fractional differential equations and fractional partial differential equations. …”
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Lie Group Method of the Diffusion Equations by Jian-Qiang Sun, Rong-Fang Huang, Xiao-Yan Gu, Ling Yu

“…The diffusion equation is discretized in spacial direction and transformed into the ordinary differential equations. The ordinary differential equations are solved by Lie group method and the explicit Runge-Kutta method. …”
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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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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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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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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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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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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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A Note on Impulsive Fractional Evolution Equations with Nondense Domain by Zufeng Zhang, Bin Liu

“…This paper is concerned with the existence of integral solutions for nondensely defined fractional functional differential equations with impulse effects. Some errors in the existing paper concerned with nondensely defined fractional differential equations are pointed out, and correct formula of integral solutions is established by using integrated semigroup and some probability densities. …”
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The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations by Abdon Atangana, Adem Kılıçman

“…We make use of the properties of the Sumudu transform to solve nonlinear fractional partial differential equations describing heat-like equation with variable coefficients. …”
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Linearization from Complex Lie Point Transformations by Sajid Ali, M. Safdar, Asghar Qadir

“…Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension d, with d≤4. …”
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High-Order Compact Implicit Difference Methods For Parabolic Equations in Geodynamo Simulation by Don Liu, Weijia Kuang, Andrew Tangborn

“…A series of compact implicit schemes of fourth and sixth orders are developed for solving differential equations involved in geodynamics simulations. …”
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Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain by Zhanrong Hu, Zhen Jin

“…A unified framework is set up to investigate the existence and uniqueness of almost automorphic mild solutions to some classes of parabolic partial differential equations and neutral functional differential equations.…”
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