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. …”
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Vieta-Lucas Collocation Technique for Examination of the Flow of Casson Fluid over a Slippery Stretching Sheet Which Is Impacted by Thermal Slip, Ohmic Dissipation, and Variable Th... by A. Eid, M. M. Khader, Ahmed M. Megahed

“…A collection of physical conditions on the sheet’s enclosing wall and the momentum and heat transport processes are expressed as partial differential equations (PDEs). Some of the similarity transformations are used to convert the collection of PDE into a system of ordinary differential equations. …”
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Finite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surface by Wubshet Ibrahim, Gosa Gadisa

“…The simultaneous nonlinear partial differential equations governing the boundary layer flow are transformed to the corresponding nonlinear ordinary differential equations using similarity solution and then solved using Galerkin finite element method (GFEM). …”
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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps by Guodong Liu, Xiaohong Wang, Xinzhu Meng, Shujing Gao

“…Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). …”
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Chemical Reaction and Radiation Effects on MHD Flow of Oldroyd-B Fluid through Porous Medium Past an Exponentially Stretching Sheet with Heat Sink by Faisal Salah, Abdelmgid O. M. Sidahmed

“…The governing system of nonlinear partial differential equations has transformed into a system of ordinary differential equations using similarity transformations. …”
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Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry by Ahmad T. Ali

“…For this, Lie group analysis method is used to identify the generators that leave the given system of nonlinear partial differential equations (NLPDEs) (Einstein field equations) invariant. …”
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Heat Transfer Analysis on the Hiemenz Flow of a Non-Newtonian Fluid: A Homotopy Method Solution by Yasir Khan, Zdeněk Šmarda

“…The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely, the homotopy perturbation method (HPM) with general form of linear operator is used to solve dimensionless nonlinear ordinary differential equations. …”
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Thermal Diffusion and Diffusion Thermo Effects on the Viscous Fluid Flow with Heat and Mass Transfer through Porous Medium over a Shrinking Sheet by Nabil Eldabe, Mahmoud Abu Zeid

“…This phenomenon is modulated mathematically by a set of partial differential equations which govern the continuity, momentum, heat, and mass. …”
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Cotton-Type and Joint Invariants for Linear Elliptic Systems by A. Aslam, F. M. Mahomed

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New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs by Norazak Senu, Mohamed Suleiman, Fudziah Ismail, Norihan Md Arifin

“…These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.…”
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Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid by Norihan Md. Arifin, Roslinda Nazar, Ioan Pop

“…The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. …”
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A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations by E. H. Doha, D. Baleanu, A. H. Bhrawy, M. A. Abdelkawy

“…Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.…”
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Stagnation Point Flow of Nanofluid over a Moving Plate with Convective Boundary Condition and Magnetohydrodynamics by Fazle Mabood, Nopparat Pochai, Stanford Shateyi

“…The governing partial differential equations for the fluid flow, temperature, and concentration are reduced to a system of nonlinear ordinary differential equations. …”
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Similarity Requirements for Mixed Convective Boundary Layer Flow over Vertical Curvilinear Porous Surfaces with Heat Generation/Absorption by Kh. Abdul Maleque

“…Similarity requirements for an incompressible fluid are sought on the basis of detailed analyses in order to reduce the governing partial differential equations into a set of ordinary differential equations. …”
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SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects by Tongqian Zhang, Xinzhu Meng, Tonghua Zhang

“…We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. …”
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Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops by F. Moriello

“…This is achieved by defining differential equations along contours connecting two fixed points, and by solving them in terms of one-dimensional generalised power series. …”
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Analysis of Metallic Nanoparticles (Cu, Al2O3, and SWCNTs) on Magnetohydrodynamics Water-Based Nanofluid through a Porous Medium by P. K. Pattnaik, S. K. Parida, S. R. Mishra, M. Ali Abbas, M. M. Bhatti

“…To formulate the mathematical modelling, similarity transformations were used, and nonlinear differential equations were obtained. To solve the formulated nonlinear differential equations, the Runge–Kutta fourth-order numerical scheme is used in conjunction with the shooting technique. …”
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Research of Nonlinear Dynamic Characteristics of Shield Machine Multilevel Planetary Gear Train by Ren Jianqing, Yu Qinghuan, Yao Jiantao, Sun Xiaoyu

“…The relative displacement between the various parts of the meshing point is derived,the system differential equation is established,the coordinate transformation of differential equations,and the non dimensional treatment is carried out. …”
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The Effects of MHD Flow and Heat Transfer for the UCM Fluid over a Stretching Surface in Presence of Thermal Radiation by M. Subhas Abel, Jagadish V. Tawade, Jyoti N. Shinde

“…The governing system of partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and is solved numerically by efficient shooting technique. …”
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Spectral framework using modified shifted Chebyshev polynomials of the third-kind for numerical solutions of one- and two-dimensional hyperbolic telegraph equations by S. M. Sayed, A. S. Mohamed, E. M. Abo-Eldahab, Y. H. Youssri

“…The current algorithm is simple to set up and is better suited to solving certain difficult partial differential equations.…”
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