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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Thermal and solutal performance analysis featuring fully developed chemically reacting micro-rotational convective flow in an open-ended vertical channel by G.T. Gitte, Shreedevi Kalyan, H. Saraswathi, Vinod Kulkarni, Mohammed Jameel, Jagadish V. Tawade, Nitiraj Kulkarni, Barno Abdullaeva, Refka Ghodhbani, M. Waqas

“…The coupled nonlinear ordinary differential equations are solved using appropriate boundary constraints. …”
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Magnetohydrodynamic Peristaltic Propulsion of Casson Nanofluids With Slip Effects Over Heterogeneous Rough Channel by Hanumesh Vaidya, Fateh Mebarek‐Oudina, Rakesh Kumar, C. Rajashekhar, Kerehalli Vinayaka Prasad, Sangeeta Kalal, Kottakkaran Sooppy Nisar

“…A novel rough non‐uniform model is effectively governed by a set of nonlinear coupled governing partial differential equations, which are simplified under long wavelength and creeping flow approximations. …”
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Influence of titanium and gold platelet morphology on heat transfer in biomagnetic third-grade hybrid nanofluid flow through a vertical channel by S. Suneetha, S.R.R. Reddy, Maduru Lakshmi Rupa, T. Mahesh Kumar, Mohammed Jameel, Taoufik Saidani, Lamia Abu El Maati, Dilsora Abduvalieva, M. Ijaz Khan

“…Through the use of perturbation, the nonlinear momentum and energy equations are reduced to nonlinear ordinary differential equations. The collocation method is utilized to solve these transformed equations. …”
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Extrapolation of cavitation and hydrodynamic pressure in lubricated contacts: a physics-informed neural network approach by Faras Brumand-Poor, Freddy Kokou Azanledji, Nils Plückhahn, Florian Barlog, Lukas Boden, Katharina Schmitz

“…In particular, physics-informed neural networks (PINNs) are as effective hybrid solvers that combine data-driven and physics-based methods to solve the partial differential equations that drive EHL simulations. By integrating physical laws into the parameter optimization of the neural network (NN), PINNs provide accurate and fast solutions. …”
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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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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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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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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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MHD radiative mixed convective flow of a sodium alginate-based hybrid nanofluid over a convectively heated extending sheet with Joule heating by Yasmin Humaira, Bossly Rawan, Alduais Fuad S., Al-Bossly Afrah, Saeed Anwar

“…The physical phenomena are modeled in a nonlinear partial differential equation, which is then converted into ordinary differential equations with the help of suitable similarity variables. …”
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Two-phase Agrawal hybrid nanofluid flow for thermal and solutal transport fluxes induced by a permeable stretching/shrinking disk by Hatem Gasmi, Muhammad Waqas, Umair Khan, Aurang Zaib, Anuar Ishak, Imtiaz Khan, Ali Elrashidi, Mohammed Zakarya

“…Through the utilization of similarity ansatz, the governing partial differential equations are simplified into a class of ordinary differential (similarity) equations. …”
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A computational role of blood nanofluid induced by a stenosed artery with porous medium and thermophoretic particle deposition effects by Shivalila Hangaragi, N. Neelima, N. Beemkumar, Ankur Kulshreshta, Umair Khan, Noreen Sher Akbar, Mohammad Kanan, Mona Mahmoud

“…Based on these assumptions, the governing equations are formulated and transformed into a system of ordinary differential equations using appropriate similarity transformations. …”
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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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