Global Dynamics of Secondary DENV Infection with Diffusion by A. M. Elaiw, A. S. Alofi

“…In this study, we develop and investigate a partial differential equations (PDEs) model that describes the dynamics of secondary DENV infection taking into account the spatial mobility of DENV particles and cells. …”
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RETRACTED: Dynamics of MHD Convection of Walters B Viscoelastic Fluid through an Accelerating Permeable Surface Using the Soret–Dufour Mechanism by P. Anusha, M. Naga Swapna Sri, Vallabhaneni Venkata Venu Madhav, Ch. Sri Chaitanya, V.V. Spandana, Kuldeep K. Saxena, Dalael Saad Abdul-Zahra, Emanoil Linul, Chander Prakash, Dharam Buddhi, Raul Campilho

“…The flow equation constitutes a set of partial differential equations (PDEs) to elucidate the real flow of a non-Newtonian liquid. …”
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Important Issues on Spectral Properties of a Transmission Eigenvalue Problem by Besiana Cobani, Aurora Simoni, Ledia Subashi

“…Nowadays, inverse scattering is an important field of interest for many mathematicians who deal with partial differential equations theory, and the research in inverse scattering is in continuous progress. …”
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Investigation of Two-Dimensional Viscoelastic Fluid with Nonuniform Heat Generation over Permeable Stretching Sheet with Slip Condition by Haroon Ur Rasheed, Zeeshan Khan, Saeed Islam, Ilyas Khan, Juan L. G. Guirao, Waris Khan

“…Here, in this research article, we have investigated an incompressible viscoelastic fluid flow over a uniform stretching surface sheet along with slip boundary conditions in the presence of porous media. The partial differential equations which govern the fluid flow are changed into ordinary differential equations through suitable similarity transformation variables. …”
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The Exact Endoscopic Effect on the Peristaltic Flow of a Nanofluid by S. M. Khaled, Abdelhalim Ebaid, Fahd Al Mutairi

“…The mathematical model is governed by a system of linear and nonlinear partial differential equations with prescribed boundary conditions. …”
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Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique by Aliaa Burqan, Mona Khandaqji, Zeyad Al-Zhour, Ahmad El-Ajou, Tasneem Alrahamneh

“…The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. …”
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A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation by Muhammad Abid, Madiha Bibi, Nasir Yasin, Muhammad Shahid

“…Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time stepping to solve the heat diffusion equation and analyze method performance.The Poisson equation is discretized using second-order central finite differences and solved with the conjugate gradient approach to determine the steady state solution. …”
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Significance of Marangoni convection in ethylene glycol base hybrid nanofluid flow with viscous dissipation through a porous medium by Ali Rehman, Ilyas Khan, Sultan Alshehery, Muhammad Sabaoon Khan

“…The authors applied appropriate transformations to convert a collection of dimension form of nonlinear partial differential equations to dimensionless form of nonlinear ordinary differential equations. …”
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Conciliating accuracy and efficiency to empower engineering based on performance: a short journey by Chinesta, Francisco, Cueto, Elias

“…The art of modeling for describing the behavior of complex systems from the solution of partial differential equations that are expected to govern their responses. …”
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Combined Effect of Buoyancy Force and Navier Slip on MHD Flow of a Nanofluid over a Convectively Heated Vertical Porous Plate by Winifred Nduku Mutuku-Njane, Oluwole Daniel Makinde

“…A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. …”
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THERMO-MAGNETO-ELASTIC ANALYSIS IN A CURRENT-CARRYING SHELL WITH CLAMPED PERIMETERS by BIAN YuHong, ZHANG Chen

“…The nonlinear partial differential equations including 10 basic unknown variables were established.Using Newmark’s stable finite equidifferent formulas,normal type which can be solved by the discrete-orthogonalization method was obtained. …”
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Analysis of an HIV infection model incorporating latency age and infection age by Jinliang Wang, Xiu Dong

“…There is a growing interest to understand impacts of latent infection age and infection age on viral infection dynamics by using ordinary and partial differential equations. On one hand, activation of latently infected cells needs specificity antigen, and latently infected CD4+ T cells are often heterogeneous, which depends on how frequently they encountered antigens, how much time they need to be preferentially activated and quickly removed from the reservoir. …”
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Bernstein Collocation Method for Solving MHD Jeffery–Hamel Blood Flow Problem with Error Estimations by Ahmad Sami Bataineh, Osman Rasit Isik, Ishak Hashim

“…The flow model described by nonlinear partial differential equations is first transformed to a third-order one-dimensional equation. …”
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Dynamic Response of Shear-Flexible Cylindrical Isotropic Shells with Clamped Edges by Zafer I. Sakka, Jamal A. Abdalla, H.R.H. Kabir

“…The Sander’s kinematic relations for moderately thick cylindrical shell panels are utilized to develop the governing partial differential equations in conjunction with the boundary conditions. …”
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Novel Evaluation of Fuzzy Fractional Helmholtz Equations by Meshari Alesemi, Naveed Iqbal, Noorolhuda Wyal

“…It is critical to emphasize that the purpose of the proposed fuzziness approach is to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations that arise in complex and physical structures.…”
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Numerical Solutions for Laminar Boundary Layer Nanofluid Flow along with a Moving Cylinder with Heat Generation, Thermal Radiation, and Slip Parameter by Titilayo Morenike Agbaje, Gilbert Makanda

“…The fluid mathematical model developed from the Navier-Stokes equations resulted in a system of partial differential equations which were then solved by the multidomain bivariate spectral quasilinearization method (MD-BSQLM). …”
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Flap/Lag Stall Flutter Control of Large-Scale Wind Turbine Blade Based on Robust H2 Controller by Tingrui Liu, Wei Xu

“…The aeroelastic partial differential equations are reduced by Galerkin method, with the aerodynamic forces decomposed by strip theory. …”
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Novel Analysis of Fuzzy Fractional Klein-Gordon Model via Semianalytical Method by Mohammad Alshammari, Wael W. Mohammed, Mohammed Yar

“…It is crucial to emphasize that the suggested fuzziness method is intended to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations found in complex and physical structures.…”
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Insight on the complete process of photoacoustic generation and propagation of cerebrovascular in brain via multi-physics coupling method by Shangkun Hou, Anzhi Lv, Jiabin Lin, Bokang You, Shuaixin Huang, Xianlin Song

“…The diffusion equation is approximated by the partial differential equations in the form of coefficients in the mathematical module of COMSOL to describe laser propagation in brain tissue. …”
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Analytical Analysis of Effects of Buoyancy, Internal Heat Generation, Magnetic Field, and Thermal Radiation on a Boundary Layer over a Vertical Plate with a Convective Surface Boun... by Solomon Bati Kejela, Mitiku Daba Firdi

“…The governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations with the help of similarity transformation which were solved analytically by applying the optimal homotopy asymptotic method. …”
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