Double diffusive MHD stagnation point flow of second grade fluid in non-Darcy porous media under radiation effects by Walid Aich, Amir Abbas, Adebowale Martins Obalalu, Walid Hassen, Lotfi Ben Said, Rejab Hajlaoui, Lioua Kolsi

“…Mathematical models are developed for the current situation and translated into a set of ordinary differential equations that are solved using MATLAB’s bvp4c. …”
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Mean field limits of co-evolutionary signed heterogeneous networks by Marios Antonios Gkogkas, Christian Kuehn, Chuang Xu

“…The approach is based on our formulation of a generalisation of the co-evolutionary network as a hybrid system of ODEs and measure differential equations parametrised by a vertex variable, together with an analogue of the variation of parameters formula, as well as the generalised Neunzert’s in-cell-particle method developed in [Kuehn, Xu. …”
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Presenting two new methods for solving linear interval optimal control problems using the resilience approach of control signal by Elnaz Hosseini, Mehdi Allahdadi, Samaneh Soradi-Zeid

“…Purpose: In this paper, two new methods are presented to find the optimal control of systems described by linear differential equations that have interval coefficients. In these methods, the given interval optimal control problem is transformed into a non-interval (deterministic) optimal control problem so that it is possible to use the optimal control theory to solve it. …”
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Exploring novel solitary wave phenomena in Klein–Gordon equation using $$\phi ^{6}$$ ϕ 6 model expansion method by Yasir A. Madani, Khidir Shaib Mohamed, Sadia Yasin, Sehrish Ramzan, Khaled Aldwoah, Mohammed Hassan

“…The $$\phi ^{6}$$ ϕ 6 model expansion technique is exceptionally adaptable and may be utilised for a wide array of nonlinear partial differential equations. Despite its versatility, the technique may not be applicable to all nonlinear PDEs, especially those that do not meet the specified requirements or structures manageable by this technique. …”
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Randomized radial basis function neural network for solving multiscale elliptic equations by Yuhang Wu, Ziyuan Liu, Wenjun Sun, Xu Qian

“…Ordinary deep neural network (DNN)-based methods frequently encounter difficulties when tackling multiscale and high-frequency partial differential equations. To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic equations. …”
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A holistic physics-informed neural network solution for precise destruction of breast tumors using focused ultrasound on a realistic breast model by Salman Lari, Hossein Rajabzadeh, Mohammad Kohandel, Hyock Ju Kwon

“…Additionally, employing PINN for estimating partial differential equations (PDE) solutions can notably decrease the enormous number of discretized elements needed. …”
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Direct and Indirect Protection with Pediatric Quadrivalent Live-Attenuated Influenza Vaccination in Europe Estimated by a Dynamic Transmission Model by Laetitia Gerlier, Judith Hackett, Richard Lawson, Sofia Dos Santos Mendes, Catherine Weil-Olivier, Markus Schwehm, Martin Eichner

“…**Methods:** A deterministic, age-structured, dynamic model was used to simulate influenza transmission across 14 European countries, comparing current vaccination coverage using a quadrivalent inactivated vaccine (QIV) to a scenario whereby vaccination coverage was extended to 50% of 2–17 year-old children, using QLAIV. Differential equations described demographic changes, exposure to infectious individuals, recovery and immunity dynamics. …”
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Numerical computation of PDE formed characterizing thermal rheology of Cu/Al2O3/TiO2 ternary nanoparticles flow between coaxial cylinders by Noreen Sher Akbar, M.Fiaz Hussain, Dennis Ling Chuan Ching, Muhammad Farooq, Ilyas Khan

“…The governing partial differential equations associated with the single-phase simulation of ternary nanoparticles, including morphological effects, are analyzed. …”
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Modeling the co-infection of HTLV-2 and HIV-1 in vivo by A. M. Elaiw, E. A. Almohaimeed, A. D. Hobiny

“…Six ordinary differential equations made up the model, which depicted the interactions between uninfected CD4+ T cells, HIV-1-infected CD4+ T cells, HIV-1 particles, uninfected CD8+ T cells, HTLV-2-infected CD8+ T cells, and HIV-1-specific B cells. …”
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Chemical effects on ecological interactions within a model-experiment loop by Lamonica, Dominique, Charles, Sandrine, Clément, Bernard, Lopes, Christelle

“…We modelled the dynamics of the three species and their interactions using a mechanistic model based on coupled ordinary differential equations. The main processes occurring in this three-species microcosm were thus formalized, including growth and settling of algae, growth of duckweeds, interspecific competition between algae and duckweeds, growth, survival and grazing of daphnids, as well as cadmium effects. …”
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Numerical Analysis on the Storage of Nuclear Waste in Gas-Saturated Deep Coal Seam by Teng Teng, Yuming Wang, Xiaoyan Zhu, Xiangyang Zhang, Sihai Yi, Guowei Fan, Bin Liu

“…As the second step, a finite element numerical model and numerical simulation are developed to analyze the storage of nuclear waste in a gas-saturated deep coal seam based on the partial differential equations (PDE) solver of COMSOL Multiphysics with MATLAB. …”
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ANFIS-PSO analysis on axisymmetric tetra hybrid nanofluid flow of Cu-CNT-Graphene-Tio2 with WEG-Blood under linear thermal radiation and inclined magnetic field: A bio-medicine app... by Maddina Dinesh kumar, José Luis Díaz Palencia, G. Dharmaiah, A. Wakif, S. Noeiaghdam, U. Fernandez-Gamiz, S. Dinarvand

“…Method: Applying the ODE45 integration technique to the given numerical solutions yields non-linear, non-dimensionalized, and highly partial differential equations that control the momentum, energy, and concentration. …”
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Nonlinear Modelling of Kinetic Data Obtained from Photocatalytic Mineralisation of 2,4-Dichlorophenol on a Titanium Dioxide Membrane by Ignazio Renato Bellobono, Roberto Scotti, Massimiliano D'Arienzo, Franca Morazzoni, Riccardo Bianchi, Rodica Stanescu, Cristina Costache, Liliana Bobirica, Gabriela Cobzaru, Paola Maria Tozzi, Mauro Rossi, Mauro Luigi Bonardi, Flavia Groppi, Luigi Gini

“…For the first series of experiments, a kinetic model was employed, already validated in previous work, from which, by a set of differential equations, four final optimised parameters, k1 and K1, k2 and K2, were calculated. …”
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Development on Lua of a software module for determining the drop point of uncontrolled cargo from UAV of aircraft type with Ardupilot control system by Andrіi Humennyi, Pavlo Malashta, Serhii Oliynick, Oleksandr Pidlisnyi, Vitalii Aleinikov

“…Known software modules for determining the point of discharge of UAVs, as a rule, perform a cyclic solution of a complex system of differential equations of cargo motion, which requires significant hardware resources. …”
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Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone by Christophe Bonneville, Nathan Bieberdorf, Arun Hegde, Mark Asta, Habib N. Najm, Laurent Capolungo, Cosmin Safta

“…However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. …”
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Entropy generation and heat convection analysis of second-grade viscoelastic nanofluid flow in a tilted lid-driven square enclosure: A finite difference approach by Anil Ahlawat, Mukesh Kumar Sharma, K. Loganathan

“…The stream function approach removes the pressure gradient term from the linear momentum equation, and the resulting partial differential equations are discretized via finite differences and then resulting algebraic equations are solved with SOR and SUR methods employing self-developed MATLAB codes. …”
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Community behavior for mathematical model of coronavirus disease 2019 (COVID-19) by M. Ramli, M. Mukramati, M. Ikhwan, H. Hafnani

“…The model-generated equation system is a nonlinear system of differential equations. The developed model is examined by determining the equilibrium point and the basic reproduction number.FINDINGS: The model resulted an asymptotically stable disease-free equilibrium and endemic equilibrium. …”
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Influence of Irradiance, Flow Rate, Reactor Geometry, and Photopromoter Concentration in Mineralization Kinetics of Methane in Air and in Aqueous Solutions by Photocatalytic Membra... by Ignazio Renato Bellobono, Mauro Rossi, Andrea Testino, Franca Morazzoni, Riccardo Bianchi, Giulia de Martini, Paola Maria Tozzi, Rodica Stanescu, Cristina Costache, Liliana Bobirica, Mauro Luigi Bonardi, Flavia Groppi

“…A kinetic model was employed, from which, by a set of differential equations, four final optimised parameters, k1 and K1, k2 and K2, were calculated, which is able to fit the whole kinetic profile adequately. …”
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DigiLoCS: A leap forward in predictive organ-on-chip simulations. by Manoja Rajalakshmi Aravindakshan, Chittaranjan Mandal, Alex Pothen, Stephan Schaller, Christian Maass

“…Our approach involves the creation of a compartmental physiological model of the liver using ordinary differential equations (ODEs) to estimate pharmacokinetic (PK) parameters related to on-chip liver clearance. …”
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Integrate mathematical modeling for heat dynamics in two-phase casson fluid flow through renal tubes with variable wall properties by P. Deepalakshmi, Adil Darvesh, Hakim AL Garalleh, Manuel Sánchez-Chero, G. Shankar, E.P. Siva

“…In order to simulate the motion of both fluids and particles, non-linear partial differential equations were employed. The flow through the ureter is exposed to evenly distributed magnetic field in the transverse direction. …”
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