Application of DTM to heat source/sink in squeezing flow of iron oxide polymer nanofluid between electromagnetic surfaces by Reshu Gupta, A.B. Albidah, NFM Noor, Ilyas Khan

“…The governing partial differential equations (PDEs) for flow, heat, and mass transfer are transformed into nonlinear ordinary differential equations (ODEs) through the appropriate similarity transformation. …”
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Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions by M. G. Sobamowo, A. T. Akinshilo, A. A. Yinusa

“…Similarity variables are used to transform the developed governing systems of nonlinear partial differential equations to systems of nonlinear ordinary differential equations. …”
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Solving Parabolic and Hyperbolic Equations with Variable Coefficients Using Space-Time Localized Radial Basis Function Collocation Method by Mohammed Hamaidi, Ahmed Naji, Ahmed Taik

“…The advantages of such formulation are (i) time discretization as implicit, explicit, θ-method, method-of-line approach, and others are not applied; (ii) the time stability analysis is not discussed; and (iii) recomputation of the resulting matrix at each time level as done for other methods for solving partial differential equations (PDEs) with variable coefficients is avoided and the matrix is computed once. …”
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Exact solutions for the Cahn–Hilliard equation in terms of Weierstrass-elliptic and Jacobi-elliptic functions by Akhtar Hussain, Tarek F. Ibrahim, F. M. Osman Birkea, Abeer M. Alotaibi, Bushra R. Al-Sinan, Herbert Mukalazi

“…Abstract Despite the historical position of the F-expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods. …”
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New super and shock like solitary structures for KdV equation with higher-order nonlinearity by H.S. Alayachi, Abdulghani Alharbi, E.K. El-Shewy, Mahmoud A.E. Abdelrahman

“…The modified F-expansion approach is an effective, powerful and straightforward method for obtaining the solitary wave solutions to the nonlinear partial differential equations (NPDEs). The effect of model parameters on the nature, properties and structures of the model solutions have been examined. …”
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Exploring the implications of ternary Jeffrey nanofluid on pulsating flow and heat transfer through unsymmetrical corrugated micro conduit by Mohamed S. Abdel-wahed, Khaled S. Mekheimer, Ahmed Y. Sayed, Shaaban I. Ahmed

“…Using the perturbation method and Mathematica software, we derived semi-analytical solutions for the governing partial differential equations in their complex form. nanoparticle-enhanced blood exhibits improved thermal performance compared to pure fluid, with the type and concentration of nanoparticles (Fe3O4, Au, SWCNTs) significantly impacting heat dissipation and temperature distribution within the microfluidic conduit. …”
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Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative by Attiya Nazneen, Rashid Nawaz, Laiq Zada, Nasir Ali, Mohamed Benghanem, Hijaz Ahmad

“…The method has been successfully applied to the higher dimension fractional order Partial differential equations and some fruitful results have been achieved. …”
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MHD Williamson Nanofluid Flow over a Stretching Sheet through a Porous Medium under Effects of Joule Heating, Nonlinear Thermal Radiation, Heat Generation/Absorption, and Chemical... by J. Bouslimi, M. Omri, R. A. Mohamed, K. H. Mahmoud, S. M. Abo-Dahab, M. S. Soliman

“…The system of nonlinear partial differential equations governing the study of fluid flow has transformed into a system of ordinary differential equations using similarity transformations and nondimensional variables which were subsequently solved numerically by using the Rung-Kutta fourth-order method with shooting technique. …”
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Analytical study of steady state axisymmetric stagnation-point gold–blood Casson nanofluid through a rotating stretchable disk by Usman Ali, Hamid Khan, Waris Khan, Emad E. Mahmoud, Marouan Kouki, Jabr Aljedani, Hakim AL Garalleh

“…By using scaling variables, the complex system of partial differential equations is simplified into a set of coupled high degree nonlinear ordinary differential equations with convective boundary conditions. …”
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The significance of magnetized thermal radiation on the magnetohydrodynamic (MHD) behavior of Williamson hybrid ferrofluids over a stretching sheet by D. Thenmozhi, M. Eswara Rao, P.D. Selvi, RLV. Renuka Devi, S. Kiranmaiye, Ch. Nagalakshmi

“…The study is mathematically modeled using partial differential equations (PDEs) accounting for the deformation vortices of a stretching surface. …”
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MOVIMENTO BROWNIANO: APLICAÇÃO EM ESTRATÉGIAS DE BUSCA by Matheus Dias Carvalho, Ricardo de Carvalho Falcão, Antonio Marcos de Oliveira Siqueira

“…This paper structured partial differential equations governing this process for the immortal case of walker, and later found analytical solutions to these expressions. …”
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Analysis of a Two-Phase MHD Free Convection Generalized Water–Ethylene Glycol (50 : 50) Dusty Brinkman-Type Nanofluid Pass through Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…While the left plate moves at a consistent velocity and the right plate stays stationary, the fluid is also evenly dispersed with all dust particles that have a spherical form. Partial differential equations (PDE) are used to present the mathematical modeling. …”
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Using Nonlinear Diffusion Model to Identify Music Signals by Qiang Li

“…In this paper, combined with the partial differential equation music signal smoothing model, a new music signal recognition model is proposed. …”
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New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques by Umair Asghar, Muhammad Imran Asjad, Yasser Salah Hamed, Ali Akgul, Murad Khan Hassani

“…These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. By transforming the original partial differential equation into an ordinary differential equation using an appropriate transformation, various types of solitary wave solutions are obtained. …”
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Stochastic Diffusive Modeling of CO₂ Emissions with Population and Energy Dynamics by Muhammad Shoaib Arif, Kamaleldin Abodayeh, Hisham M. Al-Khawar, Yasir Nawaz

“…A novel numerical scheme, an extension of the Euler-Maruyama algorithm, is proposed to solve stochastic time-dependent partial differential equations governing the model. The scheme's consistency and stability are rigorously analyzed in the mean square sense. …”
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Computational analysis of bioconvective MHD hybrid nanofluid flow of non-Newtonian fluid over cone/plate: A study based on the Cattaneo-Christov heat and mass flux model by P. Francis, P. Sambath, S. Noeiaghdam, U. Fernandez-Gamiz, S. Dinarvand

“…A similarity transformation is used to simplify the complex partial differential equations into ordinary differential equations, which are then solved using the Keller Box finite difference method. …”
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Spatially Distributed Morphogen Production and Morphogen Gradient Formation by Arthur D. Lander, Qing Nie, Frederic Y. M. Wan

“…Partial differential equations and auxiliaryconditions governing the activities of the morphogen Dpp in Drosophila wingimaginal discs were formulated and analyzed as Systems B, R, and C in[7][9][10]. …”
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Heat transport efficiency in rheology of radiated casson material due to porous shrinking cylinder by Muhammad Yasir, N. Ameer Ahammad, Aisha M. Alqahtani, Yahia Said

“…The physical characteristics of the problem are governed by partial differential equations, which are converted to ordinary differential equations using appropriate similarity variables. …”
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Entropy Analysis of Carreau Nanofluid Flow in the Presence of Joule Heating and Viscous Dissipation Past Unsteady Stretching Cylinder by Eshetu Haile Gorfie, Gizachew Bayou Zegeye, Gurju Awgichew Zergaw

“…The governing partial differential equations are transformed into first‐order initial value problems by similarity transformation and linearization. …”
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Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution by Ghani Khan, Muhammad Safdar, Safia Taj, Adnan Munir, Muhammad Tauseef Nasir

“…Twelve Lie point symmetries for the nonlinear partial differential equations describing the considered flow and heat transfer phenomena are derived. …”
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