Heat and mass transfer performance of power-law nanofluid flow with thermal radiation and joule heating aspects: Surface heat flux analysis by Mhamed Benaissa, Zia Ullah, A. Dahshan, Md Mahbub Alam, Khadijah M. Abualnaja, Hanaa Abu-Zinadah, Abdullah A. Faqihi, Nidhal Ben Khedher

“…The physical problems are converted into a nonlinear ordinary differential equation under the implementation of similarity transformations, stream functions and Keller box method. …”
Get full text

Measurement of Coordinated and Coupled Development and Evaluation of Sustainable Development for Marine Economic-Ecological Complex System by Mingming Wen, Chang Liu, K. A. Mamonov, Jun Du

“…Specifically, an ecology-dominated coordinated development model was proposed for the complex system, and a differential equation model was established to describe the dynamic coordinated development of the complex system. …”
Get full text

Probing the diversity of kink solitons in nonlinear generalised Zakharov-Kuznetsov-Benjamin-Bona-Mahony dynamical model by Naher Mohammed A. Alsafri, Hamad Zogan

“…Using a wave transformation, the employed transformative technique first converts GZK-BBME to a nonlinear ordinary differential equation (NODE). With the incorporation of the Riccati equation, a close-form solution is then assumed for the resultant NODE by RMESEM, which converts the NODE into a set of algebraic equations. …”
Get full text

Modeling and Dynamic Performance Analysis of Hydraulic Top Drive Main Transmission System with Long Hydraulic Pipelines by Yuanling Shi, Pingsong Zhang

“…A mathematical model of hydraulic top drive main transmission with differential equation of hydraulic units and state space equation of hydraulic long pipelines was deduced in this research. …”
Get full text

Large-Eddy Simulation of the Flow Past a Circular Cylinder at Re = 130,000: Effects of Numerical Platforms and Single- and Double-Precision Arithmetic by Dmitry A. Lysenko

“…Numerical simulations of sub-critical flow past a circular cylinder at Reynolds number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi></mrow></mrow></semantics></math></inline-formula> = 130,000 are performed using two numerical platforms: the commercial, Ansys Fluent, and the open-source, OpenFOAM (finite volume method and large-eddy simulation based on a differential equation for the sub-grid kinetic energy). An overview of the available experimental data and similar large-eddy simulation studies is presented. …”
Get full text

Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study by Sacrifice Nana-Kyere, Baba Seidu, Kwara Nantomah

“…With the ongoing vaccination programs for vector-borne diseases, the research proposes a nonlinear differential equation model for the malaria disease that provides public health with a shift from the classical understanding of nonpharmaceutical preventive malaria control to pharmaceutical measures of vaccines. …”
Get full text

Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term by Yuefeng Han, Xinguang Zhang, Lishan Liu, Yonghong Wu

“…By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu=p(t)f(t,u(t),u′′(t))-g(t,u(t),u′′(t)),0<t<1,α1u(0)-β1u'(0)=0,γ1u(1)+δ1u'(1)=0,α2u′′(0)-β2u′′′(0)=0,γ2u′′(1)+δ2u′′′(1)=0, with αi,βi,γi,δi≥0 and βiγi+αiγi+αiδi>0,    i=1,2, where L denotes the linear operator Lu:=(ru′′′)'-qu′′,r∈C1([0,1],(0,+∞)), and q∈C([0,1],[0,+∞)). …”
Get full text

Study on Quality Decisions in Supply Chain considering the Lagged Time and Retailers Competition by Yuan Peng, Liang Ning

“…This paper probes into the lagged time of quality on goodwill under the competitive environment of retailers and constructs a lagged differential equation of quality on goodwill based on the Nerlove–Arrow model. …”
Get full text

On the Optimal Control of HIV-TB Co-Infection and Improvement of Workplace Productivity by Baba Seidu, Oluwole Daniel Makinde, Ibrahim Yakubu Seini

“…In this paper, we present a nonlinear ordinary differential equation model to study the dynamics of HIV-TB co-infection and its effect on workforce productivity. …”
Get full text

Neural ODEs for holographic transport models without translation symmetry by Zhuo-Fan Gu, Yu-Kun Yan, Shao-Feng Wu

“…We convert the flow equation to a Neural Ordinary Differential Equation (Neural ODE), which is a neural network with continuous depth and produces output through a black-box ODE solver. …”
Get full text

Application of Adaptive Image Restoration Algorithm Based on Sparsity of Block Structure in Environmental Art Design by Bo Liang, Xin-xin Jia, Yuan Lu

“…This paper proposes a color image restoration method that adaptively determines the size of dictionary atoms and discusses a model based on the partial differential equation restoration method. Through simulation experiments combined with subjective and objective standards, the repair results are evaluated and analyzed. …”
Get full text

A Novel Procedure in Scrutinizing a Cantilever Beam with Tip Mass: Analytic and Bifurcation by Asma Alanazy, Galal M. Moatimid, T. S. Amer, Mona A. A. Mohamed, M. K. Abohamer

“…He’s frequency formula (HFF) is utilized with the non-perturbative approach (NPA) to transform the nonlinear governing ordinary differential equation (ODE) into a linear form. Mathematica Software 12.0.0.0 (MS) is employed to confirm the high accuracy between the nonlinear and the linear ODE. …”
Get full text

Development of a computational model of glucose toxicity in the progression of diabetes mellitus by Danilo T. Pérez-Rivera, Verónica L. Torres-Torres, Abraham E. Torres-Colón, Mayteé Cruz-Aponte

“…One large stride that is being made is the generation of techniques to assist physicians to ``personalize medicine''.From available physiological data, biological understanding of the system, and dimensional analysis, a differential equation-based mathematical model was built in a sequential matter, to be able to elucidate clearly how each parameter correlates to the patient's current physiological state. …”
Get full text

A Novel Version of HPM Coupled with the PSEM Method for Solving the Blasius Problem by Uriel Filobello-Nino, Hector Vazquez-Leal, Jesus Huerta-Chua, Victor Manuel Jimenez-Fernandez, Mario Alberto Sandoval-Hernandez, Enrique Delgado-Alvarado, Victor Manuel Tlapa-Carrera

“…This work studies the nonlinear differential equation that models the Blasius problem (BP) which is of great importance in fluid dynamics. …”
Get full text

Traffic Anomaly Detection Algorithm for Wireless Sensor Networks Based on Improved Exploitation of the GM(1,1) Model by Qin Yu, Jibin Lyu, Lirui Jiang, Longjiang Li

“…Based on our systematical researches on the characteristics of WSN traffic, the causes of WSN abnormal traffic, and latest related research and development, we better exploit the GM(1,1) model following four guidelines: using a sliding window to determine historical data for modeling, optimizing initial value of one-order grey differential equation, making traffic prediction by short step exponential weighted average method, and judging whether the traffic of the next moment is abnormal by Euclidean distance. …”
Get full text

Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations by Brenton T. Hall, Ching-Shan Chou, Jen-Ping Chen

“…Partial Differential Equation simulations can produce large amounts of data. …”
Get full text

Partial Volume Reduction by Interpolation with Reverse Diffusion by Olivier Salvado, Claudia M. Hillenbrand, David L. Wilson

“…The gray level of each subvoxel is considered as “material” able to move between subvoxels but not between voxels. A partial differential equation is written to allow the material to flow towards the highest gradient direction, creating a “reverse” diffusion process. …”
Get full text

Numerical Simulation of Thermo-Hydro-Mechanical Coupling of Model Test for Nuclear Waste Disposal by Yu-Ping Wang, Zhe Wang, Fa-Cheng Yi, Lei Fu, Ying Luo

“…Using the buffer material Mock-up test of multi-field coupling as a model, the partial differential equation (PDE) module in the general finite element software COMSOL Multiphysics was developed by a second development stage. …”
Get full text

A deep-learning approach to parameter fitting for a lithium metal battery cycling model, validated with experimental cell cycling time series by Maria Grazia Quarta, Ivonne Sgura, Elisa Emanuele, Jacopo Strada, Raquel Barreira, Benedetto Bozzini

“…This study contributes to shedding light on this highly technologically relevant problem, thanks to the combination of quantitative data exploitation and Partial Differential Equation (PDE) modelling for metal anode cycling. …”
Get full text

A Hybrid Renewable Sources Implementation for a DC Microgrid with Flatness-Nonlinear Control to Achieve Efficient Energy Management Strategy by Furqan A. Abbas, Adel A.Obed, Ammar Alhasiri, Salam J. Yaqoob

“…Because of the nonlinear system's behavior, differential flatness-based control has been applied mainly in nonlinear systems where the number of variables to the outputs is reduced with a robust control system established through inherited parameter reductions and equality constraints due to the system trajectories (x, u) is straightforwardly estimated from flat output trajectories y and their derivatives without any differential equation integration. The PI control is executed when the SC adjusts the DC bus voltage variation. …”
Get full text