Numerical analysis of mathematical model of nanofluid flow through stagnation point involving thermal radiation, activation energy, and living organisms by Munaza Chaudhry, Muhammad Abdul Basit, Muhammad Imran, Madeeha Tahir, Aiedh Mrisi Alharthi, Jihad Younis

“…Nonlinear partial differential equations are transformed into a collection of linked ordinary differential equations via similarity transformations. …”
Get full text

Theoretical analysis of MHD Maxwell two phase nano flow subject to viscous dissipation and chemical reaction: A nonsimilar approach by Muhammad Idrees Afridi, Gurram Dharmaiah, Jupudi Lakshmi Rama Prasad, Nallapati Vedavathi

“…Moreover, the rheological behaviours of the nanofluids are significant in defining them for convective heat transfer. The partial differential equations describe the problem, and after applying suitable transformations, it is finally transformed into a set of non-similar, nonlinear and coupled non-dimensional ordinary differential equations. …”
Get full text

Gyrotatic dynamics of magneto viscoelastic material with thermal and solutal transport by Muhammad, Masood Khan, A.S. Alqahtani, M.Y. Malik

“…The controlling model of the governing equations is converted from partial differential equations into dimensionless form in terms of ordinary differential equations by using the similarity transformations approach. …”
Get full text

A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets by Amr Ismail, Mostafa Herajy, Elsayed Atlam, Monika Heiner

“…The traditional approach to construct and simulate 3D models is to build a system of partial differential equations (PDEs). Although this approach may be computationally efficient and has been employed by many researchers over the years, it is not always intuitive since it does not provide a visual depiction of the modelled systems. …”
Get full text

Mathematical Modeling of Wax Deposition in Field-Scale Crude Oil Pipeline Systems by Francis Oketch Ochieng, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Phineas Roy Kiogora

“…The coupled nonlinear partial differential equations governing the flow are discretized in time by a second-order semi-implicit time discretization scheme based on the Adams-Bashforth and Crank-Nicolson methods, which completely decouples the computation of the governing equations. …”
Get full text

Thermal effects of ternary Casson nanofluid flow over a stretching sheet: An investigation of Thomson and Troian velocity slip by Musharafa Saleem, A. Al-Zubaidi, Neyara Radwan, S. Saleem, Hind Adawi

“…This leads to a set of partial differential equations (PDEs) based mathematical models transformed into ordinary differential equations (ODEs)-appropriate similarity transformation. …”
Get full text

Modeling Highly Buoyant Flows in the Castel Giorgio: Torre Alfina Deep Geothermal Reservoir by Giorgio Volpi, Fabien Magri, Francesca Colucci, Thomas Fisher, Mattia De Caro, Giovanni B. Crosta

“…The open source finite-element code OpenGeoSys is applied to solve the coupled systems of partial differential equations. The commercial software FEFLOW® is also used as additional numerical constraint. …”
Get full text

Computational analysis for efficient thermal transportation of ternary hybrid nanofluid flow across a stretching sheet with Cattaneo-Christov heat flux model by Wei Li, Shan Ali Khan, Muhammad Shafqat, Qamar Abbas, Taseer Muhammad, Muhammad Imran

“…The phenomenon were designed as partial differential equations. These are condensed to system of ODEs via similarity transformations. …”
Get full text

Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations by Brenton T. Hall, Ching-Shan Chou, Jen-Ping Chen

“…Partial Differential Equation simulations can produce large amounts of data. …”
Get full text

Novel numerical and artificial neural computing with experimental validation towards unsteady micropolar nanofluid flow across a Riga plate by Muhammad Bilal, F. Maiz, Muhammad Farooq, Hijaz Ahmad, Mohammad Khalid Nasrat, Hassan Ali Ghazwani

“…The fluid flow has been expressed in the form of a nonlinear system of PDEs (partial differential equations), which are reduced into the non-dimensional form of ordinary differential (ODEs) by employing the similarity transformation approach. …”
Get full text

Chemical reaction and Soret impacts on MHD heat and mass transfer Casson hybrid nanofluid (MoS2+ZnO) flow based on engine oil across a stretching sheet with radiation by M. Radhika, Y. Dharmendar Reddy

“…The relevant similarity variables convert the governing nonlinear partial differential equations to ordinary differential equations (ODEs). …”
Get full text

On the transitory performance of mixed convective heat and mass transfer around spherical region in the presence of fluctuating streams by Hossam A. Nabwey, Sahar Anwar, Muhammad Ashraf, A.M. Rashad

“…For this purpose, the coupled partial differential equations are first non-dimensionalized and their steady and oscillatory components are separated. …”
Get full text

Effects of heat generation and absorption on thermal radiative MHD flow of chemically reacting Casson nanofluids over a wedge by S. Venkateswarlu, B. Hari Babu, M. Veera Krishna

“…The basic governing partial differential equations are converting into nonlinear ordinary differential equations with employing suitable similarity transformations. …”
Get full text

Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications by Y. Alkhimenkov, Y. Y. Podladchikov

“…<p>The accelerated pseudo-transient (APT) method is a matrix-free approach used to solve partial differential equations (PDEs), characterized by its reliance on local operations, which makes it highly suitable for parallelization. …”
Get full text

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. …”
Get full text

Optimization using response surface methodology for Eyring-powell fluid flow with Cattaneo-Christov heat flux and cross diffusion effects by Pradeep Kumar, Vidhya K G, Felicita Almeida, Qasem Al-Mdallal

“…Using similarity transformations, the governing partial differential equations are converted into ordinary differential equations, which are numerically solved using the Runge-Kutta-Fehlberg 4th-5th order method. …”
Get full text

A ternary hybrid model for analysis of enhanced heat transport in non-Newtonian nanofluid over cylindrical geometry with effect of infinite shear rate viscosity by Hakim AL Garalleh

“…Based on assumptions of current study, the governing partial differential equations (PDEs) are formed and then transformed into ODEs for numerical solution. …”
Get full text

A Novel Numerical Treatment to One Dimensional Heat and Wave Equations with Second Order Accuracy by Muhammad Abid, Muhammad Shahid

“…Numerical solutions to partial differential equations (PDEs) play a vital role in modeling complex physical phenomena across scientific computing and engineering disciplines. …”
Get full text

Qualitative financial modelling in fractal dimensions by Rami Ahmad El-Nabulsi, Waranont Anukool

“…Abstract The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets. …”
Get full text

Thermal radiation and thermo-diffusion in Casson-ferrofluid over a magnetized porous surface: RSM analysis by S. Manjunatha, J. Santhosh Kumar, Khalil Ur Rehman, Wasfi Shatanawi, S.V.K. Varma

“…Similarity transformations convert the flow model's governing nonlinear coupled partial differential equations into ordinary coupled differential equations. …”
Get full text