Importance of Activation Energy on Magnetized Dissipative Casson-Maxwell Fluid through Porous Medium Incorporating Chemical Reaction, Joule Heating, and Soret Effects: Numerical St... by Nesreen Althobaiti

“…The method transforms partial differential equations originating in fluidic systems into nonlinear differential equation systems with the proper degree of similarity which is subsequently resolved utilizing the Lobatto IIIA technique’s powerful computing capabilities. …”
Get full text

Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules by Mohamed Rossafi, Roumaissae Eljazzar, Ram Mohapatra

Get full text

Improvement of Image Compression by Changing the Mathematical Equation Style in Communication Systems by Riyadh M. Al-Saleem, Yasameen A. Ghani, Shihab A. Shawkat

“…The test images for these patterns showed a discrepancy in the image resolution when the compression coefficient was increased, as the results using three types of image compression methods proved a clear superiority when using “partial differential equations (PDE)”.…”
Get full text

Evolution-Operator-Based Single-Step Method for Image Processing

“…The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. …”
Get full text

Finite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surface by Wubshet Ibrahim, Gosa Gadisa

“…The simultaneous nonlinear partial differential equations governing the boundary layer flow are transformed to the corresponding nonlinear ordinary differential equations using similarity solution and then solved using Galerkin finite element method (GFEM). …”
Get full text

Representation of the solution of a nonlinear molecular beam epitaxy equation by Boubaker Smii

“…Stochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. …”
Get full text

A Novel Approach with Comparative Computational Simulation of Analytical Solutions of Fractional Order Volterra Type Integral Equations by Javed Iqbal, Khurram Shabbir, Liliana Guran, Homan Emadifer

“…And then, by using the proposed method we solve a class of integral equations, especially fractional order Volterra type integro-partial-differential equations occurring in different fields of natural and social sciences. …”
Get full text

Chemical Reaction and Radiation Effects on MHD Flow of Oldroyd-B Fluid through Porous Medium Past an Exponentially Stretching Sheet with Heat Sink by Faisal Salah, Abdelmgid O. M. Sidahmed

“…The governing system of nonlinear partial differential equations has transformed into a system of ordinary differential equations using similarity transformations. …”
Get full text

A synthesized view of the CSF-blood barrier and its surgical implications for aging disorders by Birra Taha, Robert McGovern, Cornelius Lam, Cornelius Lam

“…We briefly review the mathematical framework for CSF transport as described by a set of well-studied partial differential equations. Moreover, we describe the major contributors of CSF flow through both diffusive and convective forces beginning at the molecular level and extending into macroscopic clinical observations. …”
Get full text

On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows by S. S. Motsa

“…This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. …”
Get full text

Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry by Ahmad T. Ali

“…For this, Lie group analysis method is used to identify the generators that leave the given system of nonlinear partial differential equations (NLPDEs) (Einstein field equations) invariant. …”
Get full text

Thermal Diffusion and Diffusion Thermo Effects on the Viscous Fluid Flow with Heat and Mass Transfer through Porous Medium over a Shrinking Sheet by Nabil Eldabe, Mahmoud Abu Zeid

“…This phenomenon is modulated mathematically by a set of partial differential equations which govern the continuity, momentum, heat, and mass. …”
Get full text

Natural Frequency Analysis of Two Nonlinear Panels Coupled with a Cavity Using the Approximate Elliptic Integral Solution and the Method of Harmonic Residual Minimization by Y. Y. Lee

“…A multistructural/acoustic modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibrations of the flexible panels and acoustic pressure induced within the air gap. …”
Get full text

Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid by Norihan Md. Arifin, Roslinda Nazar, Ioan Pop

“…The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. …”
Get full text

Modeling and Analysis of Unsteady Casson Fluid Flow due to an Exponentially Accelerating Plate with Thermal and Solutal Convective Boundary Conditions by Mehari Fentahun Endalew, Subharthi Sarkar

“…Fundamental equations governing an isotropic incompressible radiative Casson fluid flow are defined through a set of linear partial differential equations, and exact solutions are derived by using the Laplace transform approach. …”
Get full text

Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver by R. Mahmood, N. Kousar, M. Yaqub, K. Jabeen

“…All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations.…”
Get full text

A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations by E. H. Doha, D. Baleanu, A. H. Bhrawy, M. A. Abdelkawy

“…Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.…”
Get full text

New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation by Yu-Ming Chu, Shumaila Javeed, Dumitru Baleanu, Sidra Riaz, Hadi Rezazadeh

“…This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). …”
Get full text

Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters by Uzair Ahmed, Daoud Suleiman Mashat, Dalal Adnan Maturi

“…The efficiency of solving computationally partial differential equations can be illustrated by using a precise numerical method that yields remarkable precision at a low cost. …”
Get full text

Stagnation Point Flow of Nanofluid over a Moving Plate with Convective Boundary Condition and Magnetohydrodynamics by Fazle Mabood, Nopparat Pochai, Stanford Shateyi

“…The governing partial differential equations for the fluid flow, temperature, and concentration are reduced to a system of nonlinear ordinary differential equations. …”
Get full text