New Phase-Fitted and Amplification-Fitted Fourth-Order and Fifth-Order Runge-Kutta-Nyström Methods for Oscillatory Problems by K. W. Moo, N. Senu, F. Ismail, M. Suleiman

“…Two new Runge-Kutta-Nyström (RKN) methods are constructed for solving second-order differential equations with oscillatory solutions. These two new methods are constructed based on two existing RKN methods. …”
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Evolution-Operator-Based Single-Step Method for Image Processing

“…The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. …”
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A Mathematical Model for DNA Damage and Repair by Philip S. Crooke, Fritz F. Parl

“…The model encompasses a set of differential equations representing the sequence of enzymatic reactions in both damage and repair pathways. …”
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On Fitting Of Mathematical Models Of Cell Signaling Pathways Using Adjoint Systems by Krzysztof Fujarewicz, Marek Kimmel, Andrzej Swierniak

“…Such models frequently take the form of a set ofnonlinear ordinary differential equations. While the model is continuous-time,the performance index, used in the fitting procedure, involves measurementstaken only at discrete-time moments. …”
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Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics by Mei Yan, Yongfeng Li, Zhongyi Xiang

“…In order to better control the pests, two-time delayed stage-structured predator-prey models with birth pulse and pest control tactics are proposed and analyzed by using impulsive differential equations in present work. The stability threshold conditions for the mature prey-eradication periodic solutions of two models are derived, respectively. …”
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Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions by F. A. Rihan, M. Safan, M. A. Abdeen, D. Abdel Rahman

“…We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. …”
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A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories by V. V. Zozulya

“…Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. …”
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Representation of the solution of a nonlinear molecular beam epitaxy equation by Boubaker Smii

“…Stochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. …”
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Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation by Zhengwen Yin, Yuanshun Tan

“…In addition to establishing the existence and uniqueness of the global positive solution of the model, we derived the threshold conditions for the extinction and persistence of the disease using the comparison theorem and It$ \hat{o} $'s formula of stochastic differential equations. Subsequently, we obtained the asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the deterministic model corresponding to the stochastic model through stochastic stability theory. …”
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Existence Results for an Implicit Coupled System Involving $\xi$-Caputo and $p$-Laplacian Operators by Walid Benhadda, Abderrazak Kassidi, Ali El Mfadel, Elomari M'hamed

“…This paper aims to establish the existence and uniqueness of a solution to a coupled system of $\xi$-Caputo fractional differential equations involving the $p$-Laplacian operator in an arbitrary Banach space. …”
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Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels by Salvatore Brischetto

“…The exact solution is developed for the differential equations of equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. …”
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Pharmacodynamics of interspecies interactions in polymicrobial infections by C. Herzberg, J. G. C. van Hasselt

“…To this end, we developed an in silico model which combined agent-based modeling with ordinary differential equations. Our analyses suggest that both interspecies interactions, modifying either drug sensitivity or bacterial growth rate, and drug-specific pharmacological properties drive the bacterial pharmacodynamic response. …”
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Determination of Number of Infected Cells and Concentration of Viral Particles in Plasma during HIV-1 Infections Using Shehu Transformation by M. Higazy, Sudhanshu Aggarwal, Y. S. Hamed

“…The mathematical model of HIV-1 infections contains a system of two simultaneous ordinary linear differential equations with initial conditions. Results depict that Shehu transformation is very effective integral transformation for determining the number of infected cells and concentration of viral particles in plasma during HIV-1 infections.…”
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Competition and Dispersal Delays in Patchy Environments by Nancy Azer, P. van den Driessche

“…The model is formulated as a system of integro-differential equations with an arbitrary distribution of dispersal times between patches. …”
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In Situ Bioremediation of Crude Petroleum Oil Polluted Soil Using Mathematical Experimentation by Modupe Elizabeth Ojewumi, Moses Eterigho Emetere, Damilola Elizabeth Babatunde, Joshua Olusegun Okeniyi

“…The parabolic partial differential equation developed was resolved into a system of ordinary differential equations (ODEs) by orthogonal collocation method and the necessary boundary condition was used. …”
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Liquid Sloshing in a Horizontal Circular Container with Eccentric Tube under External Excitation by Mohammad Nezami, Mohammad Mehdi Mohammadi, Atta Oveisi

“…The resulting linear sets of ordinary differential equations are truncated and then solved numerically by employing Laplace transform technique followed by Durbin’s numerical inversion pattern. …”
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A leaky integrate-and-fire model with adaptation for the generation of a spike train by Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora

“…We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. …”
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Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations) by Dimitrios E. Panayotounakos, Theodoros I. Zarmpoutis

“…We provide a new mathematical technique leading to the construction of the exact parametric or closed form solutions of the classes of Abel's nonlinear differential equations (ODEs) of the first kind. These solutions are given implicitly in terms of Bessel functions of the first and the second kind (Neumann functions), as well as of the free member of the considered ODE; the parameter 𝜈 being introduced furnishes the order of the above Bessel functions and defines also the desired solutions of the considered ODE as one-parameter family of surfaces. …”
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A synthesized view of the CSF-blood barrier and its surgical implications for aging disorders by Birra Taha, Robert McGovern, Cornelius Lam, Cornelius Lam

“…We briefly review the mathematical framework for CSF transport as described by a set of well-studied partial differential equations. Moreover, we describe the major contributors of CSF flow through both diffusive and convective forces beginning at the molecular level and extending into macroscopic clinical observations. …”
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On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows by S. S. Motsa

“…This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. …”
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