Optimal System, Reductions, and Conservation Laws of a Nonlinear Damped Klein-Gordon- Fock Equation by Faiza Arif, F. M. Mahomed, F. D. Zaman, M. T. Mustafa

“…Using the similarity transformation method, the above-mentioned partial differential equation is reduced into a set of ordinary differential equations. …”
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Method for Calculating Transients in a Gas Pipeline by A. S. Fikov

“…An analytical solution of a system of partial differential equations describing the unsteady isothermal flow of real gases in gas pipelines is considered. …”
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High-resolution analysis of hydraulic response characteristics of silted stormwater pipeline and manholes in urban catchments using GASM-TranGRU and CFD-DEM by Danyang Di, Ruoyi Wang, Hongyuan Fang, Mingsheng Shi, Bin Sun, Niannian Wang, Bin Li

“…The vibrational differential equation of the ‘silted pipeline-manhole' system is then adopted to quantify the physical boundary constraints on the fluid–solid coupling relationship. …”
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Graded transcendental functions: an application to four-point amplitudes with one off-shell leg by Thomas Gehrmann, Johannes Henn, Petr Jakubčík, Jungwon Lim, Cesare Carlo Mella, Nikolaos Syrrakos, Lorenzo Tancredi, William J. Torres Bobadilla

“…We describe the derivation of canonical differential equation systems and present a method for fixing boundary conditions without the need for a full functional representation. …”
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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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Optimized Direct Padé and HPM for Solving Equation of Oxygen Diffusion in a Spherical Cell by M. A. Sandoval-Hernandez, H. Vazquez-Leal, A. Sarmiento-Reyes, U. Filobello-Nino, F. Castro-Gonzalez, A. L. Herrera-May, R. A. Callejas-Molina, R. Ruiz-Gomez

“…This work presents the application of homotopy perturbation method (HPM) and Optimized Direct Padé (ODP) to obtain a handy and easily computable approximate solution of the nonlinear differential equation to model the oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. …”
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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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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 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. …”
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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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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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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. …”
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MHD radiative mixed convective flow of a sodium alginate-based hybrid nanofluid over a convectively heated extending sheet with Joule heating by Yasmin Humaira, Bossly Rawan, Alduais Fuad S., Al-Bossly Afrah, Saeed Anwar

“…The physical phenomena are modeled in a nonlinear partial differential equation, which is then converted into ordinary differential equations with the help of suitable similarity variables. …”
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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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