Brownian motion and thermophoresis influence in magnetized Maxwell upper-convected stagnation point fluid flow via a stretching porous surface by Samson A. Agunbiade, Abayomi A. Ayoade, Timothy L. Oyekunle, Mojeed T. Akolade

“…The resulting nonlinear partial differential equations are transformed into ordinary differential equations (ODEs) using similarity variables. …”
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Transient Magnetohydrodynamic Free Convective Heat and Mass Transfer Flow with Thermophoresis past a Radiate Inclined Permeable Plate in the Presence of Variable Chemical Reaction... by M. S. Alam, M. M. Rahman, M. A. Sattar

“…The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations, which are solved numerically using a sixth-order Runge-Kutta integration scheme with Nachtsheim-Swigert shooting method. …”
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Numerical Investigation of Joule Heating Effect on Micropolar Nanofluid Flow Over an Inclined Surface in Presence of Heat Source by Keshab Borah, Jadav Konch, Shyamanta Chakraborty, Abhijit Konch, Salma Akhtar

“…This study uses similarity transformations to convert nonlinear partial differential equations that governs the flow to ordinary differential equations. …”
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Numerical Simulation of Magnetohydrodynamic Forced Convective Boundary Layer Flow past a Stretching/Shrinking Sheet Prescribed with Variable Heat Flux in the Presence of Heat Sourc... by S. P. Anjali Devi, J. Wilfred Samuel Raj

“…The basic boundary layer momentum and heat transfer equations, which are nonlinear partial differential equations, are converted into nonlinear ordinary differential equations by means of similarity transformation. …”
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Mixed convection flow with non-uniform heat source/sink in a doubly stratified magnetonanofluid by K. Mehmood, S. Hussain, M. Sagheer

“…Governing system of nonlinear partial differential equations is converted into a system of nonlinear ordinary differential equations. …”
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Numerical Modeling Chemical Vapor Infiltration of SiC Composites by Yaochan Zhu, Eckart Schnack

“…The model consists of a set of nonlinear partial differential equations by coupling Ginzburg-Landau type phase field equations with mass balance equations (e.g., convection-diffusion equation) and the modified Navier-Stokes equations which accounts for the fluid motion. …”
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Impact of chemical reaction on the Cattaneo–Christov heat flux model for viscoelastic flow over an exponentially stretching sheet by Abdelmgid O. M. Sidahmed, Faisal Salah, K. K. Viswanathan

“…Using similarity transformation, the controlling system of nonlinear partial differential equations was transformed into a system of ordinary differential equations. …”
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Magnetohydrodynamics stagnation-point flow of a nanofluid past a stretching/shrinking sheet with induced magnetic field: a revised model by Junoh, Mohamad Mustaqim, Md. Ali, Fadzilah, Pop, Ioan

“…A similarity transformation with symmetry variables are introduced in order to alter from the governing nonlinear partial differential equations into a nonlinear ordinary differential equations. …”
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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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Exploration of nonlinear traveling wave phenomena in quintic conformable Benney-Lin equation within a liquid film by Noorah Mshary

“…The proposed transformation-based approach developed for nonlinear partial differential equations (PDEs) and fractional PDEs (FPDEs), efficiently produces a plethora of traveling wave solutions for the targeted CBLE, capturing the system's nuanced dynamics. …”
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Viscoelastic thermal nanofluid flow and heat mass transfer due to a stretching sheet with slip velocity phenomenon and convective heating by Mohammed Alrehili

“…The governing equations of the model, which are nonlinear partial differential equations, are first modified via dimensionless transformation. …”
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Multidimensional Exact Solutions of a System of Nonlinear Boussinesq Type Equations by A.A. Kosov, E.I. Semenov, V. V. Tirskikh

“…We study the system of two nonlinear partial differential equations of the fourth order. The right parts of the system of equations contain multidimensional analogs of Boussinesq equation, expressed in terms of two-fold Laplace operators and squares of gradients of the required functions, as well as linear functions of the relationship. …”
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QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments by Y. H. Yamazaki, P. L. Read, S. R. Lewis, T. W. N. Haine, P. D. Williams

“…The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. …”
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Hydromagnetic Mixed Convective Nanofluid Slip Flow past an Inclined Stretching Plate in the Presence of Internal Heat Absorption and Suction by S. P. Anjali Devi, P Suriyakumar

“…Similarity transformations are employed to transform the governing nonlinear partial differential equations into coupled non-linear ordinary differential equations. …”
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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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Enhancing the Heat Transfer Due to Hybrid Nanofluid Flow Induced by a Porous Rotary Disk with Hall and Heat Generation Effects by Naif Abdulaziz M. Alkuhayli

“…The physical problem under the given configuration is reduced to a set of nonlinear partial differential equations using the conservation laws. …”
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Dynamic analysis of a cable-stayed bridge subjected to a continuous sequence of moving forces by Mitao Song, Dengqing Cao, Weidong Zhu

“…Orthogonality conditions of exact mode shapes of the linearized cable-stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear model to a set of ordinary differential equations by using the Galerkin method. …”
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A minimalist model for coevolving supply and drainage networks by Shashank Kumar Anand, Milad Hooshyar, Jan Martin Nordbotten, Amilcare Porporato

“…The model consists of three coupled, nonlinear partial differential equations that describe spatial density patterns of input and output materials by modifying a mediating scalar field, on which supply and drainage networks are carved. …”
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Faber-Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions Cost by Shu-Li Mei

“…Second, using the couple technique of the variational iteration method (VIM) and the precision integration method, the sparse approximation solution of the nonlinear partial differential equations can be obtained. The method is tested on three classical nonlinear option pricing models such as Leland model, Barles-Soner model, and risk adjusted pricing methodology. …”
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Discovering optical solutions to a nonlinear Schrödinger equation and its bifurcation and chaos analysis by Alsallami Shami A. M.

“…The pursuit of solitary wave solutions to complex nonlinear partial differential equations is gaining significance across various disciplines of nonlinear science. …”
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