Physics-Informed Denoising Model for Dynamic Data Recovery of Power Systems by Jian Li, Guoqiang Lu, Yongbin Li, Dongning Zhao, Huaiyuan Wang, Yucheng Ouyang

“…In light of the poor interpretability exhibited by traditional machine learning (ML) methods in denoising, a physics-informed denoising model (PIDM) for dynamic data recovery is proposed. The differential equations of physical models in power systems are employed to guide the training of PIDM. …”
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Investigation of Micro- and Nanosized Particle Erosion in a 90° Pipe Bend Using a Two-Phase Discrete Phase Model by M. R. Safaei, O. Mahian, F. Garoosi, K. Hooman, A. Karimipour, S. N. Kazi, S. Gharehkhani

“…The 3-D governing differential equations were discretized using finite volume method. …”
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Novel computations of the time-fractional chemical Schnakenberg mathematical model via non-singular kernel operators by Abdul Hamid Ganie, Fatemah Mofarreh, N. S. Alharthi, Adnan Khan

“…The derived results demonstrate how simple and efficient the proposed method is to apply for analysing the behaviour of fractional-order nonlinear differential equations that arise in related fields of engineering and science.…”
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A minimal mathematical model for the initial molecular interactions of death receptor signalling by Christian Winkel, Simon Neumann, Christina Surulescu, Peter Scheurich

“…We use here a mass action kinetics approach to establish an ordinary differential equations model describing the dynamics of primary ligand/receptor complex formation as a basis for further clustering on the cell membrane. …”
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The Effect of Delay Techniques on a Lassa Fever Epidemic Model by Ali Raza, Eugenio Rocha, Emad Fadhal, Rashid I. H. Ibrahim, Eman Afkar, Muhammad Bilal

“…By introducing a delay parameter and decay exponential term into the existing model in the literature, we got the system of highly nonlinear delay differential equations (DDEs). The fundamental properties such as positivity, boundedness, existence, and uniqueness are verified for the said model. …”
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BERT-Residual Quantum Language Model Inspired by ODE Multi-Step Method by Shaohui Liang, Yingkui Wang, Shuxin Chen

“…Therefore, in this paper, we propose the BERT-Residual quantum language model inspired by the multi-step method of ordinary differential equations (ODE), using the density matrix to capture the semantic high-order interaction features missing in the BERT modeling process, and obtain the sentence representation, and perform the first step Residuals. …”
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Model analysis for an HIV infectious disease using elasticity and sensitivity techniques by Honar J. Hamad, Sarbaz H. A. Khoshnaw, Muhammad Shahzad

“…The model includes a class of nonlinear ordinary differential equations, and has both infection-free and endemic infection equilibrium points. …”
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SOLUTION OF THE PROBLEM OF OIL-POOL IN-SITU COMBUSTION FRONT PROPAGATION ON THE BASIS OF HEURISTIC HYPOTHESIS REGARDING TEMPERATURE AND CONCENTRATION PROFILES by K. V. Dobrego

“…Simple algebraic and differential equations fordetermination of the temperature and concentration profiles as well as for the front propagation velocity are derived for two cases i.e. the lack of oxidizer and the fuel component fault. …”
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A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets by Amr Ismail, Mostafa Herajy, Elsayed Atlam, Monika Heiner

“…The traditional approach to construct and simulate 3D models is to build a system of partial differential equations (PDEs). Although this approach may be computationally efficient and has been employed by many researchers over the years, it is not always intuitive since it does not provide a visual depiction of the modelled systems. …”
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The significance of heat transfer through natural convection in stagnation point flow of prandtl fluid by Salman Zeb, Zakir Ullah, A.B. Albidah, Ilyas Khan, Waqar A. Khan

“…The analysis integrates velocity, concentration slips, and temperature jumps within a nonlinear partial differential equation framework. These equations are converted into nonlinear partial differential equations using appropriate dimensionless variables. …”
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MODELING OF BUSINESS PROCESSES FOR MANAGING INTEGRATIVE DIGITAL DEVELOPMENT OF ENTERPRISES by Оlena V. Vynogradova, Svitlana V. Lehominova, Aliona Yu. Goloborodko, Tetiana I. Nosova

“…The fundamental methods for modeling business process flows using mathematical and analytical tools, specifically a system of differential equations with defined initial conditions, have been substantiated, enabling the integral assessment of enterprise business process modeling. …”
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A numerical framework for computing steady states of structured population models and their stability by Inom Mirzaev, David M. Bortz

“…In particular, we use the Trotter-Kato Theorem to approximate the infinitesimal generator of an evolution equation on a finite dimensional space, which in turn reduces the evolution equation into a system of ordinary differential equations. Consequently, we approximate and study the asymptotic behavior of stationary solutions. …”
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Mathematical Modeling of Wax Deposition in Field-Scale Crude Oil Pipeline Systems by Francis Oketch Ochieng, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Phineas Roy Kiogora

“…The coupled nonlinear partial differential equations governing the flow are discretized in time by a second-order semi-implicit time discretization scheme based on the Adams-Bashforth and Crank-Nicolson methods, which completely decouples the computation of the governing equations. …”
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Asymptotic analysis of mathematical model describing a new treatment of breast cancer using AZD9496 and palbociclib by Ophir Nave, Ophir Nave

“…The mathematical model that described the interaction between the cancer cells, the treatment, and the immune system cells includes a system of nonlinear ordinary differential equations of the firs order. In general, dynamic variables of a given system change each at a different rate. …”
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Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents by Raimund BÜrger, Gerardo Chowell, Elvis GavilÁn, Pep Mulet, Luis M. Villada

“…An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. …”
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Physics-Informed Neural Network for modeling and predicting temperature fluctuations in proton exchange membrane electrolysis by Islam Zerrougui, Zhongliang Li, Daniel Hissel

“…This method solves differential equations and estimates the unknown parameters governing the temperature dynamics within the PEM electrolysis system. …”
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Mathematical Modelling of Cholera Transmission incorporating Media Coverage. by Muhereza, Obed

“…The model was thereafter analyzed using the stability theory of differential equations. The basic reproduction number Ra, was derived using the next generation matrix approach. …”
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Mixed Convective-Radiative Dissipative Magnetized Micropolar Nanofluid Flow over a Stretching Surface in Porous Media with Double Stratification and Chemical Reaction Effects: ADM-... by P. K. Pattnaik, M. M. Bhatti, S. R. Mishra, Munawwar Ali Abbas, O. Anwar Bég

“…The nonlinear governing partial differential conservation equations are rendered into nonlinear ordinary differential equations via relevant transformations. An innovative semi-numerical methodology combining the Adomian decomposition method (ADM) with Padé approximants and known as ADM-Padé is deployed to solve the emerging nonlinear ordinary differential boundary value problem with appropriate wall and free stream conditions in MATLAB software. …”
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On the transitory performance of mixed convective heat and mass transfer around spherical region in the presence of fluctuating streams by Hossam A. Nabwey, Sahar Anwar, Muhammad Ashraf, A.M. Rashad

“…For this purpose, the coupled partial differential equations are first non-dimensionalized and their steady and oscillatory components are separated. …”
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Modeling Highly Buoyant Flows in the Castel Giorgio: Torre Alfina Deep Geothermal Reservoir by Giorgio Volpi, Fabien Magri, Francesca Colucci, Thomas Fisher, Mattia De Caro, Giovanni B. Crosta

“…The open source finite-element code OpenGeoSys is applied to solve the coupled systems of partial differential equations. The commercial software FEFLOW® is also used as additional numerical constraint. …”
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