The Impact of Reduced Gravity on Oscillatory Mixed Convective Heat Transfer around a Non-Conducting Heated Circular Cylinder by Zia Ullah, Muhammad Ashraf, Ioannis E. Sarris, Theodoros E. Karakasidis

“…The fluid motion is governed by connected nonlinear partial differential equations which are converted into convenient equations by applying a finite-difference scheme with the primitive transformation and a Gaussian elimination technique. …”
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Response surface optimization and sensitive analysis on biomagnetic blood Carreau nanofluid flow in stenotic artery with motile gyrotactic microorganisms by Tao-Qian Tang, Zahir Shah, Thirupathi Thumma, Muhammad Rooman, Narcisa Vrinceanu, Mansoor H. Alshehri

“…The system's nonlinear partial differential equations are transformed into nonlinear ODEs through suitable transformations. …”
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G-Jitter effect on heat and mass transfer of three-dimensional stagnation point nanofluid flow by Ahmad Kamal, Mohamad Hidayad

“…These nonlinear partial differential equations are initially reduced into a dimensionless system of equations using the similarity transformation technique. …”
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Numerical investigation on the thermal-nanofluidic flow induced transverse and longitudinal vibrations of single and multi-walled branched nanotubes resting on nonlinear elastic fo... by A.A. Yinusa, M.G. Sobamowo, A.O. Adelaja, S.J. Ojolo, M.A. Waheed, M.A. Usman, Antonio Marcos de Oliveira Siqueira, Júlio César Costa Campos, Ridwan Ola-Gbadamosi

“…Therefore, in this present work, the developed coupled systems of nonlinear partial differential equations are solved using multi-dimensional numerical PDEs solvers coupled with PDE-tools in MATLAB. …”
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Some new soliton solutions to the (3 + 1)-dimensional generalized KdV-ZK equation via enhanced modified extended tanh-expansion approach by Romana Ashraf, Farrah Ashraf, Ali Akgül, Saher Ashraf, B. Alshahrani, Mona Mahmoud, Wajaree Weera

“…GKdV-zk techniques solutions are obtained using the improved modified extended tanh expansion method, which is one of the most efficient algebraic methods for obtaining accurate solution to nonlinear partial differential equations. We aim to show how the analyzed model’s parameter impact soliton behavior by choosing different bright and single soliton forms and by developing various analytical optical soliton solutions for the explored equation. …”
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A novel vortex dynamics for micropolar fluid flow in a lid-driven cavity with magnetic field localization – A computational approach by Shabbir Ahmad, Kashif Ali, Tanveer Sajid, Umaima Bashir, Farhan Lafta Rashid, Ravinder Kumar, Mohamed R. Ali, Ahmed S. Hendy, Adil Darvesh

“…We used a numerical method to solve the challenging nonlinear partial differential equations that arise from the mathematical modeling of the fluid flow in the presence of a magnetic field. …”
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Prediction of stream water quality in Godavari River Basin, India using statistical and artificial neural network models by Nagalapalli Satish, Jagadeesh Anmala, Rajitha K, Murari Raja Raja Varma

“…The physically based computational water quality models would require large spatial and temporal information databases of climatic, hydrologic, and environmental variables and solutions of nonlinear, partial differential equations at each grid point in a river basin. …”
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Multiple Shear-Banding Transitions for a Model of Wormlike Micellar Solutions by Zhou, Lin, Cook, L. Pamela, McKinley, Gareth H.

“…The addition of inertia into the coupled set of nonlinear partial differential equations describing the material response changes the type of the equation set, introducing a transient damped (diffusive and dispersive) inertio-elastic shear wave following the imposition of flow. …”
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A Hybrided Method for Temporal Variable-Order Fractional Partial Differential Equations with Fractional Laplace Operator by Chengyi Wang, Shichao Yi

“…In this paper, we present a more general approach based on a Picard integral scheme for nonlinear partial differential equations with a variable time-fractional derivative of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo stretchy="false">(</mo><mi mathvariant="bold">x</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>∈</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and space-fractional order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>∈</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>v</mi><mo>=</mo><msup><mi>u</mi><mo>′</mo></msup><mrow><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula> is introduced as the new unknown function and <i>u</i> is recovered using the quadrature. …”
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DYNAMICS OF A GEOMETRICALLY AND PHYSICALLY NONLINEAR SENSITIVE ELEMENT OF A NANOELECTROMECHANICAL SENSOR IN THE FORM OF AN INHOMOGENEOUS NANOBEAM IN THE TEMPERATURE AND NOISE FIELD... by Vadim A. Krysko, Irina V. Papkova, Tatiana V. Yakovleva, Alena A. Zakharova, Maksim V. Zhigalov, Anton V. Krysko

“…Methods: variation methods, a second-order finite difference method for reducing the system of nonlinear partial differential equations to the Cauchy problem, the Newmark method for solving the Cauchy problem, the Birger method of variable elasticity parameters for solving a physically non-linear problem, the variation iteration method for obtaining an analytical solution of the two-dimensional heat equation. …”
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Numerical Investigation of Double-Diffusive Convection in an Irregular Porous Cavity Subjected to Inclined Magnetic Field Using Finite Element Method by Imran Shabir Chuhan, Jing Li, Muhammad Shafiq Ahmed, Inna Samuilik, Muhammad Aqib Aslam, Malik Abdul Manan

“…Design/methodology/approach—After validating the results, the FEM (finite element method) is used to simulate the flow pattern, temperature variations, and concentration by solving the nonlinear partial differential equations with the modified Rayleigh number (10⁴ ≤ <i>Ra</i> ≤ 10⁷), Darcy number (10⁻⁴ ≤ <i>Da</i> ≤ 10⁻¹), Lewis number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0.1</mn><mo>≤</mo><mi>L</mi><mi>e</mi><mo>≤</mo><mn>10</mn><mo>)</mo></mrow></semantics></math></inline-formula>, and Hartmann number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="|"><mrow><mn>0</mn><mo>≤</mo><mi>H</mi><mi>a</mi><mo>≤</mo><mn>40</mn></mrow></mfenced></mrow></semantics></math></inline-formula> as the dimensionless operating parameters. …”
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Goal-oriented inference : theoretical foundations and application to carbon capture and storage by Lieberman, Chad Eric

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Hierarchies of the Korteweg–de Vries Equation Related to Complex Expansion and Perturbation by Tatyana V. Redkina, Arthur R. Zakinyan, Robert G. Zakinyan, Olesya B. Surneva

“…A hierarchy is understood here as a family of nonlinear partial differential equations with a Lax pair with a common scattering operator. …”
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Numerical Study of Heat and Mass Transfer for Williamson Nanofluid over Stretching/Shrinking Sheet along with Brownian and Thermophoresis Effects by Aiguo Zhu, Haider Ali, Muhammad Ishaq, Muhammad Sheraz Junaid, Jawad Raza, Muhammad Amjad

“…Employing the similarity transformations, the governing nonlinear Partial Differential Equations (PDEs) are converted into the Ordinary Differential Equations (ODEs). …”
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Steady Squeezing Flow of Magnetohydrodynamics Hybrid Nanofluid Flow Comprising Carbon Nanotube-Ferrous Oxide/Water with Suction/Injection Effect by Muhammad Sohail Khan, Sun Mei, Shabnam, Nehad Ali Shah, Jae Dong Chung, Aamir Khan, Said Anwar Shah

“…The governing equations of the proposed hybrid nanoliquid model are formulated through highly nonlinear partial differential equations (PDEs) including momentum equation, energy equation, and the magnetic field equation. …”
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Methods for Constructing Complex Solutions of Nonlinear PDEs Using Simpler Solutions by Alexander V. Aksenov, Andrei D. Polyanin

“…This paper describes a number of simple but quite effective methods for constructing exact solutions of nonlinear partial differential equations that involve a relatively small amount of intermediate calculations. …”
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Design of intelligent control system and its application on fabricated conveyor belt grain dryer by Lutfy, Omar F.

“…As a result, the mathematical models developed for these systems consist of sets of highly complex and nonlinear partial differential equations (PDEs) which require highly complicated numerical techniques to solve them. …”
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Stability of the second order partial differential equations by Ghaemi MB, Cho YJ, Alizadeh B, Gordji M Eshaghi

“…</p> <p>In this paper, by using Banach's contraction principle, we prove the stability of nonlinear partial differential equations of the following forms:</p> <p><display-formula><m:math name="1029-242X-2011-81-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow> <m:mfenced separators="" open="{" close=""> <m:mrow> <m:mtable class="gathered"> <m:mtr> <m:mtd> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">=</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>y</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-punc">,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mi>a</m:mi> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mi>b</m:mi> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>t</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">=</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>y</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-punc">,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mi>p</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> <m:mi>t</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mi>q</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>t</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:msub> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mi>t</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:msub> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>t</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">=</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>y</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-punc">,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mi>p</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mi>q</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">=</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>y</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-punc">.…”
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