Enhanced thermal and mass transfer of harnessing microbial mediation in electrically conducting Oldroyd-B nanofluid flow: Eukaryotes microorganisms in biological applications by Aaqib Majeed, Nouman Ijaz, Narjes Baazaoui, Kamal Barghout, Sadia Samar Ali, Najma Saleem, Ahmed M Hassan, Sidra Naeem

“…The boundary layer flow's highly nonlinear partial differential equations are transformed into ordinary differential equations in the study via similarity transformations. …”
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Efficient Quantum Algorithm for Nonlinear Reaction–Diffusion Equations and Energy Estimation by Liu, Jin-Peng, An, Dong, Fang, Di, Wang, Jiasu, Low, Guang H., Jordan, Stephen

“…Here we develop an efficient quantum algorithm based on Liu et al. (2021) for reaction–diffusion equations, a class of nonlinear partial differential equations (PDEs). To achieve this, we improve upon the Carleman linearization approach introduced in Liu et al. (2021) to obtain a faster convergence rate under the condition $$R_D < 1$$ R D < 1 , where $$R_D$$ R D measures the ratio of nonlinearity to dissipation using the $$\ell _{\infty }$$ ℓ ∞ norm. …”
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Localized Discrete Empirical Interpolation Method by Peherstorfer, Benjamin, Butnaru, Daniel, Willcox, Karen E., Bungartz, Hans-Joachim

“…This paper presents a new approach to construct more efficient reduced-order models for nonlinear partial differential equations with proper orthogonal decomposition and the discrete empirical interpolation method (DEIM). …”
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Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes by K. Schürholt, J. Kowalski, J. Kowalski, H. Löwe

“…This coupling has an impact on choosing efficient numerical schemes for 1D snowpack models which are naturally not designed to cope with mathematical particularities of arbitrary, nonlinear partial differential equations (PDEs). To explore this coupling we have implemented a stand-alone finite element solution of the coupled heat and mass equations in snow using the computing platform FEniCS. …”
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NEURAL NETWORK METHOD OF RESTORING AN INITIAL PROfiLE OF THE SHOCK WAVE by Tatiana A. Shemyakina, Dmitriy A. Tarkhov, Alexandra R. Beliaeva, Ildar U. Zulkarnay

“…In this paper, we apply neural network modeling to solve the inverse problem of mathematical physics with a system of nonlinear partial differential equations of hyperbolic type. In the problem, the initial conditions are unknown and are reconstructed from measurements made at a later point in time. …”
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Coaxially swirled porous disks flow simultaneously induced by mixed convection with morphological effect of metallic/metallic oxide nanoparticles by Qadeer Raza, Xiaodong Wang, Ahmed M. Hassan, Imran Siddique, Bagh Ali, Irfan Ali

“…The high-order, nonlinear, ordinary differential equations are obtained from the governing system of nonlinear partial differential equations via similarity transformation. …”
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Magnetohydrodynamics Stagnation-Point Flow of a Nanofluid Past a Stretching/Shrinking Sheet with Induced Magnetic Field: A Revised Model by Mohamad Mustaqim Junoh, Fadzilah Md Ali, Ioan Pop

“…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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Heat transfer attributes of Al2O3-Fe3O4/H2O hybrid nanofluid flow over a yawed cylinder by P.M. Patil, H.F. Shankar

“…The flow problem is modelled in terms of highly nonlinear partial differential equations (NPDEs) subject to the appropriate boundary conditions. …”
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Numerical analysis of MHD tri-hybrid nanofluid over a nonlinear stretching/shrinking sheet with heat generation/absorption and slip conditions by Zafar Mahmood, Sayed M Eldin, Khadija Rafique, Umar Khan

“…An ordinary differential equation system may be constructed from nonlinear partial differential equations for which a similarity transformation does not provide an exact solution. …”
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Coupled effects of magnetic field, number of walls, geometric imperfection, temperature change, and boundary conditions on nonlocal nonlinear vibration of carbon nanotubes resting... by M.G. Sobamowo, J.O. Akanmu, O.A. Adeleye, S.A. Akingbade, A.A. Yinusa

“…With the aids of Erigen's nonlocal elasticity, Euler-Bernoulli beam theories and van der Waal forces equation, systems of nonlinear partial differential equations governing the dynamics responses of slightly curved multi-walled carbon nanotubes resting on Winkler and Pasternak foundations in a thermal-magnetic environment are developed. …”
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Viscous dissipation and Joule heating effects of Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk by Gizachew Bayou Zegeye, Eshetu Haile, Gurju Awgichew

“…To examine the impacts of the aforementioned effects, the conservation laws are formulated with strongly nonlinear partial differential equations (PDEs), which are then transformed into a system of initial value problems (IVPs) using appropriate similarity transformations and techniques. …”
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Ionanofluid flow through a triangular grooved microchannel heat sink: Thermal heightening by I. Zahan, R. Nasrin, Salma Jahan

“…The governing equations of nonlinear partial differential equations describing the physical phenomena along with proper border settings are resolved by applying the finite element method (FEM). …”
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Essays in financial economics by Duarte, Victor (Fonseca Duarte)

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Pattern formation in multiphase models of chemotactic cell aggregation by Green, J, Whiteley, J, Oliver, J, Byrne, H, Waters, S

“…The model leads to a system of coupled nonlinear partial differential equations for the volume fraction and velocity of the cell phase, the culture medium pressure and the chemoattractant concentration, which must be solved subject to appropriate boundary and initial conditions. …”

Hybrid nanofluid flow past a biaxial stretching/shrinking permeable surface with radiation effect: Stability analysis and heat transfer optimization by Yahaya, Rusya Iryanti, Mustafa, Mohd Shafie, Md Arifin, Norihan, Pop, Ioan, Md Ali, Fadzilah, Mohamed Isa, Siti Suzilliana Putri

“…This flow problem is translated into nonlinear partial differential equations and boundary conditions. After similarity transformations, the numerical computations are conducted using the bvp4c solver. …”

Radiation and nanoparticles shape effect on aligned MHD jeffrey hybrid nanofluids flow and heat transfer over a stretching inclined plate. by Ilias, Mohd. Rijal, Rosli, Nurul Nabilah, Ishak, Siti Shuhada, David, Vincent Daniel, Shafie, Sharidan, Abd. Rahman, Mohd. Nashriq

“…The Keller Box method is used to solve numerically the Jeffrey hybrid nanofluid's governing nonlinear partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs) using similarity transformation. …”
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Heat transfer in MHD flow of maxwell fluid via fractional cattaneo-friedrich model: a finite difference approach by Saqib, Muhammad, Hanif, Hanifa, Abdeljawad, T., Khan, Ilyas, Shafie, Sharidan, Nisar, Kottakkaran Sooppy

“…The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations. Most importantly, in the nonlinear problems, either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems (without developing the fractional model even using artificial replacement) are solved. …”

Numerical approach toward ternary hybrid nanofluid flow with nonlinear heat source-sink and fourier heat flux model passing through a disk by Khaled Alqawasmi, Khalid Abdulkhaliq M. Alharbi, Umar Farooq, Sobia Noreen, Muhammad Imran, Ali Akgül, Mohammad Kanan, Jihad Asad

“…To derive dimensionless forms of regulating paired nonlinear partial differential equations, a collection of pertinent similarity transformations is used. …”
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Brownian and thermal diffusivity impact due to the Maxwell nanofluid (graphene/engine oil) flow with motile microorganisms and Joule heating by Algehyne Ebrahem A., Rehman Sadique, Ayub Rashid, Saeed Anwar, Eldin Sayed M., Galal Ahmed M.

“…In order to transform highly nonlinear partial differential equations into nonlinear ordinary differential equations, an appropriate similarity transformation is exploited. …”
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Multiple Lie symmetry solutions for effects of viscous on magnetohydrodynamic flow and heat transfer in non-Newtonian thin film by Safdar Muhammad, Taj Safia, Bilal Muhammad, Ahmed Shoaib, Khan Muhammad Ijaz, Ben Moussa Sana, Fadhl Bandar M., Makhdoum Basim M., Eldin Sayed M.

“…Numerous flow and heat transfer studies have relied on the construction of similarity transformations which map the nonlinear partial differential equations (PDEs) describing the flow and heat transfer, to ordinary differential equations (ODEs). …”
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