Experimental Validation of Numerical Model for Bi-Tilt-Isolator by Ming-Hsiang Shih, Wen-Pei Sung, Chia-Yu Ho

“…Then, BTI element of nonlinear analysis program, GENDYN, is developed by the fourth-order Runge-Kutta method, the discretized ordinary differential equation for three movement stages of BTI. Then, test set-up of superstructure installed with BTI is tested and recorded the real displacement and acceleration responses under conditions of full lubrication, mild lubrication, and without lubrication between interface of bi-tilt beveled substrate and slider with three various initial displacements. …”
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Estimating the Force of Infection with Helicobacter pylori in Japan by Taishi Kayano, Ki-Deok Lee, Hiroshi Nishiura

“…Solving the McKendrick partial differential equation model, the seroprevalence was modeled as a function of survey year and age. …”
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Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising by Khursheed Alam, Alka Chauhan, Santosh Kumar

“…The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. …”
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The relative biologic effectiveness versus linear energy transfercurve as an output-input relation for linear cellular systems by Quoc T. Luu, Paul DuChateau

“…Here we introduce a differential equation formulation for a signal-and-system model that sees cells as systems, different radiation types as input, and cellular responses as output. …”
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Temperature and state-dependent electrical conductivity of soft biological tissue at hyperthermic temperatures by Junren Ran, Martin Ostoja-Starzewski

“…Methods: We model the denaturation process with an Arrhenius-type differential equation for chemical kinetics and a modified Stogryn equation for electrical conductivity under state transition. …”
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Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials by Luc Leroy Mambou Ngueyep, Joseph Ndop, Elise Rose Atangana Nkene, Jean-Marie Bienvenu Ndjaka

“…By choosing that the inhomogeneity parameter is between -0.5 and 0.5, we have established the differential equation which describes the equilibrium of the hollow cylinder in rotation under an axial load. …”
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Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak by Tianzeng Li, Yu Wang, Weiqiu Pan

“…To provide the numerical solution of the single-term (or multiterm) fractional-order nonlinear differential equation, the GMMP scheme and Newton method are introduced. …”
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Numerical exploration and thermal criticality of a dual exothermic reaction with radiative heat loss in co-axial cylinder configurations by R.A Oderinu, S.O. Salawu, A.D. Ohaeghue, S. Alao, E.I. Akinola, J.A. Owolabi

“…Appropriate similarity variables were employed to transform the dimensional equation in a cylindrical coordinate system into dimensionless differential equation. The problem is solved using the iterative analytical method, which relies on the principle of weighted residuals. …”
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An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells by Patrick W. Nelson, Michael A. Gilchrist, Daniel Coombs, James M. Hyman, Alan S. Perelson

“…We show that this model is a generalization ofthe standard differential equation and of delay models previously used to describeHIV-1 infection, and provides a means for exploring fundamental issuesof viral production and death. …”
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Modeling the Process of Obtaining Liquid Pyrolysis Products of Plant Biomass Taking into Account the Rate of their Cooling by S. V. Vasilevich, M. V. Malko, D. V. Degterov, A. N. Asadchy

“…To assess the effect of the cooling rate of liquid pyrolysis products, a third-order differential equation was used for a model limited by the reaction rate. …”
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Dynamical Visualization and Qualitative Analysis of the (4+1)-Dimensional KdV-CBS Equation Using Lie Symmetry Analysis by Maria Luz Gandarias, Nauman Raza, Muhammad Umair, Yahya Almalki

“…By using these generators, the given model is converted into an ordinary differential equation. An adaptive approach, the generalized exp(-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">S</mi></mrow></semantics></math></inline-formula>(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula>)) expansion technique has been utilized to uncover closed-form solitary wave solutions. …”
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Newton–Simpson-based predictor–corrector methods for milling chatter stability prediction by Yongjian Ji, Xiaokang Xu, Yulin Yang, Runnan Liu, Shuyao Liu, Zhenghu Yan

“…Firstly, the milling delay differential equation is transformed into the state space form, and then the time-delayed term and the periodic coefficient matrix of the state space equation are treated as an operator. …”
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Face Boundary Formulation for Harmonic Models: Face Image Resembling by Hung-Tsai Huang, Zi-Cai Li, Yimin Wei, Ching Yee Suen

“…Mapping between the source and target face boundaries with constituent pixels is explored by two approaches: cubic spline interpolation and ordinary differential equation (ODE) using Hermite interpolation. …”
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Numerical modelling of rope elasticity for heave compensation lifting in offshore crane operations by Bassey Asanga, Akanimo Ekpenyong, Aniekan Ikpe

“…The results showed that the developed mathematical model for the wire rope extension (e) derived from second order differential equation found directly proportional to the load applied but inversely proportional to the wire rope stiffness (β)  during WOC and WC were 2.50 × 107 N.m-1 and 3.33 × 107 N.m-1, respectively. …”
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Three-Dimensional Inversion of Borehole-Surface Resistivity Method Based on the Unstructured Finite Element by Zhi Wang, Sinan Fang

“…The forward simulation and calculation start from the partial differential equation and the boundary conditions of the total potential of the three-dimensional point current source field are satisfied. …”
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A Stochastic Model for Adsorption Kinetics by Silvia Rodríguez-Narciso, Juan Antonio Lozano-Álvarez, Rogelio Salinas-Gutiérrez, Netzahualcóyotl Castañeda-Leyva

“…The developed model is the first to describe pollutant removal kinetics based on a stochastic differential equation.…”
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Thermal radiation effects of ternary hybrid nanofluid flow in the activation energy: Numerical computational approach by Hakeem Ullah, Syed Arshad Abas, Mehreen Fiza, Aasim Ullah Jan, Ali Akgul, Magda Abd El-Rahman, Seham M. Al-Mekhlafi

“…Methodology: After utilizing von Karman similarity transformations to renovate the principal equations into the set of nonlinear differential equation systems, the resulting equations were solved using the bvp4c numerical approach with the assistance of MATLAB software. …”
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Application of Image Denoising Method Based on Two-Way Coupling Diffusion Equation in Public Security Forensics by Yiqun Wang, Changpeng He, Zhenjiang Li

“…By improving the second-order partial differential equation, a new diffusion function with better diffusion effect than the original model is constructed. …”
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Integrated movement models for individual tracking and species distribution data by Frances E. Buderman, Ephraim M. Hanks, Viviana Ruiz‐Gutierrez, Michael Shull, Robert K. Murphy, David A. W. Miller

“…We outline a general IMM framework and develop and apply a specific stochastic differential equation model to a case study of telemetry and species distribution data for golden eagles in western North American during spring migration. …”
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Mathematical Modelling and Analysis of Transmission Dynamics of Lassa Fever by E. A. Bakare, E. B. Are, O. E. Abolarin, S. A. Osanyinlusi, Benitho Ngwu, Obiaderi N. Ubaka

“…In this work, a periodically forced seasonal nonautonomous system of a nonlinear ordinary differential equation is developed that captures the dynamics of Lassa fever transmission and seasonal variation in the birth of Mastomys rodents where time was measured in days to capture seasonality. …”
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