Unstructured Grids and the Multigroup Neutron Diffusion Equation by German Theler

“…It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. …”
Get full text

Nonrigid Registration of Monomodal MRI Using Linear Viscoelastic Model by Jian Yang, Yang Chen, Jingfan Fan, Songyuan Tang

“…After global registration, the local shape variations are assumed to have the properties of the Maxwell model of linear viscoelasticity, and the deformation fields are constrained by the corresponding partial differential equations. To speed up the registration, an adaptive force is introduced according to the maximum displacement of each iteration. …”
Get full text

Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations by Meilan Qiu, Liquan Mei, Dewang Li

“…The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations.…”
Get full text

Couple Stress Sodium Alginate-Based Casson Nanofluid Analysis through Fick’s and Fourier’s Laws with Inclined Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…Physically existent things utilize partial differential equations as a method of derivation. By using dimensionless variables, the underlying PDEs are dimensionless. …”
Get full text

Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment by Brandy Rapatski, Juan Tolosa

“…We investigate two HIV/AIDS epidemic models.The first model represents the early San Franciscomen having sex with men (MSM) epidemic.We use data from the San Francisco City Clinic Cohort Study (SFCCC), documentingthe onset of HIV in San Francisco (1978-1984).The second model is a ``what-if'' scenario model includingtesting and treatment in the SFCCC epidemic.We use compartmental, population-level models,described by systems ofordinary differential equations.We find the basic reproductive number $R_0$ for each system,and we prove that if $R_0<1 the="" system="" has="" only="" the="" disease-free="" equilibrium="" dfe="" which="" is="" locally="" and="" globally="" stable="" whereas="" if="" r_0="">1$, the DFE is unstable.In addition, when $R_0>1$, both systems have a unique endemic equilibrium (EE).We show that treatment alone would not have stopped the San Francisco MSM epidemic,but would have significantly reduced its impact.…”
Get full text

"MoSpec": A customized and integrated system for model development, verification and validation. by Marcello Pompa, Simona Panunzi, Alessandro Borri, Laura D'Orsi, Andrea De Gaetano

“…To facilitate the creation and sharing of such models, the CNR-IASI BioMatLab group developed the "Gemini" (MoSpec/Autocoder) system, a framework allowing researchers with basic mathematical knowledge to quickly and correctly translate biological problems into Ordinary Differential Equations models. The system facilitates the development and computation of mathematical models for the interpretation of medical and biological phenomena, also using data from the clinical setting or laboratory experiments for parameter estimation.…”
Get full text

MAC Layer Energy Consumption and Routing Protocol Optimization Algorithm for Mobile Ad Hoc Networks by Yaohua Chen, Waixi Liu

“…In order to solve the problem that the analytic solution of differential equations cannot be obtained in the model, a numerical solution of the optimization algorithm is proposed based on the implicit Runge–Kutta method. …”
Get full text

Starlikeness associated with certain strongly functions by Afis Saliu, Kanwal Jabeen, Jianhua Gong, Sarfraz Nawaz Malik, Hala Alaqad

“…It also finds the solutions to first-order differential equations and utilizes these results together with the differential subordination developed by Miller and Mocanu to obtain the conditions so that some first-order differential relations associated with ϕλ are subordinate to certain Ma and Minda functions. …”
Get full text

Numerical analysis of ice accretion on an airfoil: A case study by Lucas Farabello, Ana Scarabino, Federico Bacchi

“…The numerical analysis of ice accretion involves differential equations for the resolution of the air velocity field, the transport of droplets, and their icing and melting. …”
Get full text

Implementing the Galerkin Method Associated with the Shifted Vieta-Lucas Polynomials for Studying Numerically the Bionanofluid Flow Which Is Saturated by Gyrotactic Microorganisms... by M. M. Khader, M. M. Babatin, Ahmed M. Megahed, A. Eid

“…The shifted Vieta-Lucas polynomials are then used as basis functions on the provided domain to solve the nonlinear system of ordinary differential equations that has been constructed (ODEs). The results are presented in the form of graphs and tables to assess the impact of the problem’s governing parameters. …”
Get full text

Analyzing Axial Stress and Deformation of Tubular for Steam Injection Process in Deviated Wells Based on the Varied (T,P) Fields by Yunqiang Liu, Jiuping Xu, Shize Wang, Bin Qi

“…The varied temperature and pressure fields were researched by the coupled differential equations concerning mass, momentum, and energy equations instead of traditional methods. …”
Get full text

A Theoretical Model of Listeriosis Driven by Cross Contamination of Ready-to-Eat Food Products by C. W. Chukwu, F. Nyabadza

“…In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. …”
Get full text

Mixed Convection in a Double Lid-Driven Wavy Shaped Cavity Filled with Nanofluid Subject to Magnetic Field and Internal Heat Source by Kakali Chowdhury, Md. Abdul Alim

“…The physical problems are characterized by 2D governing partial differential equations accompanying proper boundary conditions and are discretized using Galerkin’s finite element formulation. …”
Get full text

Mathematically modeling PCR: An asymptotic approximation with potential for optimization by Martha Garlick, James Powell, David Eyre, Thomas Robbins

“…A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action and simplifying assumptions regarding the structure of the reactions. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one base pair at a time. …”
Get full text

Application of BSDE in Standard Inventory Financing Loan by Hui Zhang, Wenyu Meng, Xiaojie Wang, Jianwei Zhang

“…Applying backward stochastic differential equations (BSDEs), we get the explicit solutions of the models. …”
Get full text

A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing by Arthanari Ramesh, Alireza Bahramian, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari, Iqtadar Hussain

“…Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. …”
Get full text

Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar by M.-C. Casabán, J.-C. Cortés, B. García-Mora, L. Jódar

“…Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. …”
Get full text

AI-assisted discovery of quantitative and formal models in social science by Julia Balla, Sihao Huang, Owen Dugan, Rumen Dangovski, Marin Soljačić

“…By extending neuro-symbolic methods to find compact functions and differential equations in noisy and longitudinal data, we show that our system can be used to discover interpretable models from real-world data in economics and sociology. …”
Get full text

Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach by M. B. Almatrafi

“…The outcomes highlight the effectiveness and adaptability of the proposed strategy in resolving fractional nonlinear differential equations and expand our knowledge of fractional-order systems.…”
Get full text

Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models by Divine Wanduku, Md Mahmud Hasan

“…The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. …”
Get full text