Thermal radiation effects of ternary hybrid nanofluid flow in the activation energy: Numerical computational approach by Hakeem Ullah, Syed Arshad Abas, Mehreen Fiza, Aasim Ullah Jan, Ali Akgul, Magda Abd El-Rahman, Seham M. Al-Mekhlafi

“…Methodology: After utilizing von Karman similarity transformations to renovate the principal equations into the set of nonlinear differential equation systems, the resulting equations were solved using the bvp4c numerical approach with the assistance of MATLAB software. …”
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Physics-Informed Neural Networks for Modal Wave Field Predictions in 3D Room Acoustics by Stefan Schoder

“…PINNs are appealing since they can efficiently integrate a partial differential equation and experimental data by minimizing a loss function. …”
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Existence for Singular Periodic Problems: A Survey of Recent Results by Jifeng Chu, Juntao Sun, Patricia J. Y. Wong

“…We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.…”
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A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach by Taha Aziz, F. M. Mahomed

“…In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. …”
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Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems by P. G. Dlamini, S. S. Motsa, M. Khumalo

“…The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. …”
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SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions by Pengju Duan

“…The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. …”
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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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Generalization of neural network models for complex network dynamics by Vaiva Vasiliauskaite, Nino Antulov-Fantulin

“…Abstract Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph. …”
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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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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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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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