Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency by Rodrigue Yves M’pika Massoukou, Suares Clovis Oukouomi Noutchie, Richard Guiem

“…The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. …”
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Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells by Maria Vittoria Barbarossa, Christina Kuttler, Jonathan Zinsl

“…Our model reproduces the dynamics of three different tumor cell populations: quiescent cells,cells during the interphase and mitotic cells.Starting from a partial differential equations (PDEs) setting, a delay differential equations (DDE) model is derived for aneasier and more realistic approach.Our equations also include interactions of tumor cells with immune system effectors.We investigate the model both from the analytical and the numerical point of view, give conditions forpositivity of solutions and focus on the stability of the cancer-free equilibrium. …”
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Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling by O. D. Makinde, S. Khamis, M. S. Tshehla, O. Franks

“…The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. …”
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Peridynamic Formulation for Coupled Thermoelectric Phenomena by Migbar Assefa, Xin Lai, Lisheng Liu, Yang Liao

“…This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes at the discontinuities. …”
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Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption by Khilap Singh, Manoj Kumar

“…The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. …”
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Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink by I. Swain, S. R. Mishra, H. B. Pattanayak

“…The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. …”
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On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells by Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel

“…The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. …”
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Unsteady MHD Mixed Convection Flow of Chemically Reacting Micropolar Fluid between Porous Parallel Plates with Soret and Dufour Effects by Odelu Ojjela, N. Naresh Kumar

“…A suitable similarity transformation is used to reduce the governing partial differential equations into nonlinear ordinary differential equations and then solved numerically by the quasilinearization method. …”
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Solving arbitrary one-loop reduction via generating function by Tingfei Li, Yuekai Song, Liang Zhang

“…We first establish the partial differential equations governing the higher-pole generating function. …”
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Stagnation Point Flow of Nanofluid over a Moving Plate with Convective Boundary Condition and Magnetohydrodynamics by Fazle Mabood, Nopparat Pochai, Stanford Shateyi

“…The governing partial differential equations for the fluid flow, temperature, and concentration are reduced to a system of nonlinear ordinary differential equations. …”
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On the Regularity of the Entropy Solution of the Fractional-Semigeostrophic Equation Using Ultrafilters by Gilles Tamba Bokolo

“…This work lays the groundwork for future studies on fractional partial differential equations in geophysical contexts, potentially leading to more accurate predictive models in meteorology and oceanography.…”
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Modeling Multicellular Systems Using Subcellular Elements by T. J. Newman

“…We present here a detailed description of the model, and use successive mean-field approximations to connect it to more coarse-grained approaches, such as discrete cell-based algorithms and coupled partial differential equations. We also discuss efficient algorithms for encoding the model, and give an example of a simulation of an epithelial sheet. …”
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Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method by Haifa Bin Jebreen

“…In this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2 + 1)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of these equations in the diverse applications are described. …”
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Application of Local Fractional Homotopy Perturbation Method in Physical Problems by Nabard Habibi, Zohre Nouri

“…Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. …”
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Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation by Mehmet Emir Koksal

“…Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. …”
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Nonlinear iterative approximation of steady incompressible chemically reacting flows by Gazca-Orozco, Pablo Alexei, Heid, Pascal, Süli, Endre

“…We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is of power-law type, with a power-law index that depends on the concentration. …”
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Simulating Smoke Filling in Big Halls by Computational Fluid Dynamics by W. K. Chow, C. L. Chow, S. S. Li

“…Mathematical aspects concerning of discretization of partial differential equations and algorithms for solving the velocity-pressure linked equations are briefly outlined. …”
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A toxin-mediated size-structured population model: Finite difference approximation and well-posedness by Qihua Huang, Hao Wang

“…Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. …”
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Finite element approximation of a population spatial adaptation model by Gonzalo Galiano, Julián Velasco

“…In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. …”
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PDE Modeling of a Microfluidic Thermal Process for Genetic Analysis Application by Reza Banaei Khosroushahi, Horacio J. Marquez, Jose Martinez-Quijada, Christopher J. Backhouse

“…The general partial differential equations describing the dynamics of the system are separated into steady-state and transient parts which are derived for a carefully chosen three-dimensional axisymmetric model. …”
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