Exact Solutions for Unsteady Free Convection Flow of Casson Fluid over an Oscillating Vertical Plate with Constant Wall Temperature by Asma Khalid, Ilyas Khan, Sharidan Shafie

“…The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. …”
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Approximate Solutions of Fisher's Type Equations with Variable Coefficients by A. H. Bhrawy, M. A. Alghamdi

“…Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.…”
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$\phi $-FEM for the heat equation: optimal convergence on unfitted meshes in space by Duprez, Michel, Lleras, Vanessa, Lozinski, Alexei, Vuillemot, Killian

“…Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular background mesh, not fitting the domain and its real boundary exactly. …”
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Brief introduction to distributions and to Hörmander spaces Bp,k by Alejandro Ortiz Fernández

“…Partial differential equations (PDE’s) are, we believe, little known in our country, especially at a medium-advanced level, in particular, their historical roots and methods developed in their evolution. …”
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The General Traveling Wave Solutions of the Fisher Equation with Degree Three by Wenjun Yuan, Qiuhui Chen, Jianming Qi, Yezhou Li

“…Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.…”
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An Efficient Method for Systems of Variable Coefficient Coupled Burgers’ Equation with Time-Fractional Derivative by Hossein Aminikhah, Nasrin Malekzadeh

“…Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractional-order partial differential equations.…”
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Analysis of the Nonlinear Structural-Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods by Y. Y. Lee

“…The structural acoustic problem considered in this study is the nonlinear resonant frequencies of a rectangular tube with one open end, one flexible end, and four rigid side walls A multiacoustic single structural modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibration of the flexible end and acoustic pressure induced within the tube. …”
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On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods by A. K. Gupta, S. Saha Ray

“…Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like Burgers-Fisher and generalized Fisher equations. …”
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Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations by Azam Zahrani, Mashaallah Matinfar, Mostafa Eslami

“…This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. …”
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Influence of temperature-dependent viscosity on the MHD Couette flow of dusty fluid with heat transfer by Hazem A. Attia

“…The governing nonlinear partial differential equations are solved numerically and some important effects for the variable viscosity and the uniform magnetic field on the transient flow and heat transfer of both the fluid and dust particles are indicated.…”
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Constructions of solitary wave solutions for huge family of NPDEs with three applications. by Hanan A Alkhidhr, Y Omar

“…This study offers closed-form solutions for the frequently utilised families of nonlinear partial differential equations (NPDEs). This form based on the He's semi-inverse technique. …”
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Weyl-Euler-Lagrange Equations of Motion on Flat Manifold by Zeki Kasap

“…In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. …”
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Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions by Yan Gao, Songlin Liu

“…In addition, a fine description of the sixth-order CFD schemes is also developed for equations with constant coefficients, which is used to discuss certain partial differential equations (PDEs) with arbitrary dimensions. …”
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On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications by Teng-fei Li, Heng-you Lan

“…In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. …”
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Multiple Slip Effects on MHD Unsteady Flow Heat and Mass Transfer Impinging on Permeable Stretching Sheet with Radiation by Fazle Mabood, Stanford Shateyi

“…Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. …”
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A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme by Azmy S. Ackleh, Mark L. Delcambre, Karyn L. Sutton, Don G. Ennis

“…The model consists of a system of nonlinear hyperbolic partial differential equations coupled with three nonlinear ordinary differential equations. …”
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Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid by M. B. Akgül, G. Sarı, M. Pakdemirli

“…Adopting the obtained symmetry groups, governing partial differential equations are converted into ordinary differential equations and then solved numerically. …”
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On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs by F. N. Koumboulis, M. G. Skarpetis, B. G. Mertzios

“…The Euler equations, namely a set of nonlinear partial differential equations (PDEs), mathematically describing the dynamics of inviscid fluids are numerically integrated by directly modeling the original continuous-domain physical system by means of a discrete multidimensional passive (MD-passive) dynamic system, using principles of MD nonlinear digital filtering. …”
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A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method by R. Ellahi

“…Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. …”
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Vibration Suppression of a Coupled Aircraft Wing with Finite-Time Convergence by Yiming Liu, Zhifeng Tan, Xiaofen Yang, Xiaowei Wang

“…Since the model is modeled by partial differential equations, the traditional control design scheme based on the ordinary differential equation model is not applicable, and the control law design becomes very complex. …”
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