Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms by A. H. Bhrawy, L. M. Assas, M. A. Alghamdi

“…Since the collocation method approximates ordinary differential equations, partial differential equations, and integral equations in physical space, it is very easy to implement and adapt to various problems, including variable coefficient and nonlinear differential equations. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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). …”
Get full text

Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency by Rodrigue Yves M’pika Massoukou, Suares Clovis Oukouomi Noutchie, Richard Guiem

“…The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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. …”
Get full text

Mathematical modelling of MHD hybrid nanofluid flow in a convergent and divergent channel under variable thermal conductivity effect by Alharbi Abdulaziz H.

“…H2O{\text{H}}_{\text{2}}\text{O}) are considered in this work. The partial differential equations modelling the problem are reduced to ordinary differential equations following the application of the similarity transformations. …”
Get full text

Simulating Smoke Filling in Big Halls by Computational Fluid Dynamics by W. K. Chow, C. L. Chow, S. S. Li

“…Mathematical aspects concerning of discretization of partial differential equations and algorithms for solving the velocity-pressure linked equations are briefly outlined. …”
Get full text

Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling by O. D. Makinde, S. Khamis, M. S. Tshehla, O. Franks

“…The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. …”
Get full text

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. …”
Get full text

PDE Modeling of a Microfluidic Thermal Process for Genetic Analysis Application by Reza Banaei Khosroushahi, Horacio J. Marquez, Jose Martinez-Quijada, Christopher J. Backhouse

“…The general partial differential equations describing the dynamics of the system are separated into steady-state and transient parts which are derived for a carefully chosen three-dimensional axisymmetric model. …”
Get full text

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations by S. S. Motsa, V. M. Magagula, P. Sibanda

“…This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. …”
Get full text

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

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

Dynamical Models of Tuberculosis and Their Applications by Carlos Castillo-Chavez, Baojun Song

“…Modelformulations involve a variety of mathematical areas, such as ODEs(Ordinary Differential Equations) (both autonomous andnon-autonomous systems), PDEs (Partial Differential Equations),system of difference equations, system of integro-differentialequations, Markov chain model, and simulation models.…”
Get full text