Optimal control of agent-based models via surrogate modeling. by Luis L Fonseca, Lucas Böttcher, Borna Mehrad, Reinhard C Laubenbacher

“…For a given ABM and a given optimal control problem, the algorithm derives a surrogate model, typically lower-dimensional, in the form of a system of ordinary differential equations (ODEs), solves the control problem for the surrogate model, and then transfers the solution back to the original ABM. …”
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ON APPLICATION OF ARTIFICIAL NEURAL NETWORKS FOR MODELING OF WATER CONSUMPTION by Alexander N. Salugin, Roman N. Balkushkin

“…The use of mathematical models in the form of a system of differentiated equations is hampered by the uncertainty of the coefficients in their right-hand sides, which describe the intensities of processes of different natures: precipitation, water consumption by various sectors of the water management complex, water runoff during snow melting, transpiration, infiltration, etc. …”

BUCKLING OF BEAMS WITH A BOUNDARY ELEMENT TECHNIQUE by ABDERRAZEK MESSAOUDI, LASZLO PETER KISS

“…If the Green functions of these boundary value problems are known, the differential equations of the stability problems that contain the critical load sought can be turned into eigenvalue problems given by homogeneous Fredholm integral equations. …”
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Limit Cycles of a Class of Perturbed Differential Systems via the First-Order Averaging Method by Amor Menaceur, Salah Mahmoud Boulaaras, Amar Makhlouf, Karthikeyan Rajagobal, Mohamed Abdalla

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Computer-Aided Numerical Inversion of Laplace Transform by Umesh Kumar

“…This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.…”
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Solving Quantum Dynamics with a Lie-Algebra Decoupling Method by Sofia Qvarfort, Igor Pikovski

“…The approach involves identifying a Lie algebra that governs the dynamics of the system, enabling the derivation of differential equations to solve the Schrödinger equation. …”
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Group Classification of a Generalized Lane-Emden System by Ben Muatjetjeja, Chaudry Masood Khalique, Fazal Mahmood Mahomed

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Stability Analysis of a Class of Neural Networks with State-Dependent State Delay by Yue Chen, Jin-E Zhang

“…The differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. …”
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Epidemic Analysis and Mathematical Modelling of Influenza with Vaccination by Musiime, Catherine

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Second order slip micropolar MHD hybrid nanofluid flow over a stretching surface with uniform heat source and activation energy: Numerical computational approach by Syed Arshad Abas, Hakeem Ullah, Mehreen Fiza, Ali Akgul, Aasim Ullah Jan, Magda Abd El-Rahman, Seham M. Al-Mekhlafi

“…These PDEs are subsequently transformed into a set of ordinary differential equations (ODEs) using similarity transformations. …”
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Adaptive Hierarchical Collocation Method for Solving Fractional Population Diffusion Model by Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei

“…The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. …”
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Fixed Point Theory and the Liouville–Caputo Integro-Differential FBVP with Multiple Nonlinear Terms by Shahram Rezapour, Ali Boulfoul, Brahim Tellab, Mohammad Esmael Samei, Sina Etemad, Reny George

“…This work is reserved for the study of a special category of boundary value problems (BVPs) consisting of Liouville–Caputo integro-differential equations with multiple nonlinear terms. This fractional model and its boundary value conditions (BVCs) involve different simple BVPs, in which the second BVC as a linear combination of two Caputo derivatives of the unknown function equals a nonzero constant. …”
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Detection of the onset of numerical chaotic instabilities by lyapunov exponents by Alicia Serfaty De Markus

“…It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. …”
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The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes by Peng Li, Chuancun Yin, Ming Zhou

“…Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. …”
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Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy by Chao Yue, Tiecheng Xia

“…Then, the CCIRD equations are decomposed into Dubrovin-type ordinary differential equations. Furthermore, the theory of the trigonal curve and the properties of the three kinds of Abel differentials are applied to obtain the explicit theta function representations of the Baker-Akhiezer function and the meromorphic functions. …”
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T model of growth and its application in systems of tumor-immunedynamics by Mohammad A. Tabatabai, Wayne M. Eby, Karan P. Singh, Sejong Bae

“…We recommend usage of the T growth model forthe growth of tumors as part of any system of differential equations. Use ofthis model within a system will allow more flexibility in representing thenatural rate of tumor growth. …”
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On Modeling and Constrained Model Predictive Control of Open Irrigation Canals by Lihui Cen, Ziqiang Wu, Xiaofang Chen, Yanggui Zou, Shaohui Zhang

“…As a set of hyperbolic partial differential equations, they are not solved explicitly and difficult to design optimal control algorithms. …”
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Investigation of a spatial double pendulum: an engineering approach by S. Bendersky, B. Sandler

“…Matlab computer programs were used for solving the nonlinear differential equations by the Runge-Kutta method. Fourier transformation was used to obtain the frequency spectra for analyses of the oscillations of the two pendulums. …”
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New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation by Yu-Ming Chu, Shumaila Javeed, Dumitru Baleanu, Sidra Riaz, Hadi Rezazadeh

“…This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). …”
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SIMULATION OF OPEN MECHANISMS FOR THE ADDITIVE PROCESS WELD PLASTICS by N. N. Hurski, V. A. Skachek, A. V. Skachek, Y. A. Skudnyakov

“…This article discusses: model of the two-link mechanism; generalized scheme of mechatronic simulation model of 3D-printer with the positioning units of electric DC; mathematical model of the actuator of the printer unit in the form of a system of differential equations; 3D-printer programming model implemented in the Matlab-Simulink environment using the c standard library blocks and SimMechanics library; virtual (animated) 3D printer model on the basis of the library Simulink 3D Animation, supports the visualization of the movements of the designed mechanism of the basic units. …”
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