Modeling and Analysis of Unsteady Casson Fluid Flow due to an Exponentially Accelerating Plate with Thermal and Solutal Convective Boundary Conditions by Mehari Fentahun Endalew, Subharthi Sarkar

“…Fundamental equations governing an isotropic incompressible radiative Casson fluid flow are defined through a set of linear partial differential equations, and exact solutions are derived by using the Laplace transform approach. …”
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Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters by Uzair Ahmed, Daoud Suleiman Mashat, Dalal Adnan Maturi

“…The efficiency of solving computationally partial differential equations can be illustrated by using a precise numerical method that yields remarkable precision at a low cost. …”
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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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A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations by S. S. Motsa, V. M. Magagula, P. Sibanda

“…This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. …”
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Recent Developments on Hybrid Time-Frequency Numerical Simulation Techniques for RF and Microwave Applications by Jorge F. Oliveira, José C. Pedro

“…This apparent multirate behavior can be appropriately described using partial differential equations (PDEs) within a bivariate framework, which can be solved in an efficient way using hybrid time-frequency techniques. …”
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Nonrigid Registration of Monomodal MRI Using Linear Viscoelastic Model by Jian Yang, Yang Chen, Jingfan Fan, Songyuan Tang

“…After global registration, the local shape variations are assumed to have the properties of the Maxwell model of linear viscoelasticity, and the deformation fields are constrained by the corresponding partial differential equations. To speed up the registration, an adaptive force is introduced according to the maximum displacement of each iteration. …”
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Estimates for Unimodular Multipliers on Modulation Hardy Spaces by Jiecheng Chen, Dashan Fan, Lijing Sun, Chunjie Zhang

“…Finally, we investigate the boundedness of the operator eit|Δ|α/2 for α>0 and obtain the local well-posedness for the Cauchy problem of some nonlinear partial differential equations with fundamental semigroup eit|Δ|α/2.…”
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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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Analysis of the n-Term Klein-Gordon Equations in Cantor Sets by Nikhil Sharma, Sunil Joshi, Pranay Goswami

“…In conclusion, the fractional complex transform with the local fractional differential transform method has been proven to be a robust and flexible approach towards obtaining effective approximate solutions of local fractional partial differential equations.…”
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Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms by A. H. Bhrawy, L. M. Assas, M. A. Alghamdi

“…Since the collocation method approximates ordinary differential equations, partial differential equations, and integral equations in physical space, it is very easy to implement and adapt to various problems, including variable coefficient and nonlinear differential equations. …”
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The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses by Yohan Chandrasukmana, Helena Margaretha, Kie Van Ivanky Saputra

“…This paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation. …”
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Thermal and Flow Dynamics of Magnetohydrodynamic Burgers' Fluid Induced by a Stretching Cylinder with Internal Heat Generation and Absorption by Fateh Mebarek-Oudina, G. Dharmaiah, J.L. Rama Prasad, H. Vaidya, Manda Aruna Kumari

“…By applying boundary layer theory, we transform the governing partial differential equations into a standard system of ordinary differential equations through similarity transformations. …”
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Numerical Study on Resistance Change Characteristics of Phase Change Materials by Yifang Su, Yihang Zhang, Kaifeng Lin, Guanjun Zhao, Qinzheng Yu, Zuoqi Hu, Xiongfei Tao

“…To study the characteristics of the phase change materials, a numerical simulation model of the resistive change unit based on the finite element method and the classic nucleation/growth theory is established, while the partial differential equations of electricity and heat conduction and the discrete formula of the finite element are also derived. …”
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Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System by Alejandro Marquez, Jairo José Espinosa Oviedo, Darci Odloak

“…Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. …”
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Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative by Attiya Nazneen, Rashid Nawaz, Laiq Zada, Nasir Ali, Mohamed Benghanem, Hijaz Ahmad

“…The method has been successfully applied to the higher dimension fractional order Partial differential equations and some fruitful results have been achieved. …”
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An efficient technique to study of time fractional Whitham–Broer–Kaup equations by Nishant Bhatnagar, Kanak Modi, Lokesh Kumar Yadav, Ravi Shanker Dubey

“…The method’s novelty and straightforward implementation establish it as a reliable and efficient analytical technique for solving both linear and nonlinear fractional partial differential equations.…”
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STABILITY RESEARCH OF FLOW-INDUCED VIBRATION OF HYBRID RIGID-FLEXIBLE PIPE CONVEYING FLUID (MT) by LIU MingJun, ZHANG ZhenJiu, YANG XianQing, Lü JianXing, LI YueAn

“…Based on Hamilton′s principle, the governing equations of motion of the hybrid rigid-flexible pipe system were established. The partial differential equations of motion were discretized via Galerkin′s approach using the modal functions of a cantilevered beam. …”
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Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method by Wafaa B. Rabie, Hamdy M. Ahmed, Taher A. Nofal, E. M. Mohamed

“…Higher-order nonlinear partial differential equations, such as the eighth-order Kac-Wakimoto model, are useful for studying wave turbulence in fluids, where energy transfers across a range of wave numbers. …”
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Nonlinear Dynamic Analysis of Macrofiber Composites Laminated Shells by Xiangying Guo, Dameng Liu, Wei Zhang, Lin Sun, Shuping Chen

“…The vibration mode-shape functions are obtained according to the boundary conditions, and then the Galerkin method is employed to transform partial differential equations into two nonlinear ordinary differential equations. …”
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Circular thin plates buckling analysis with HRPIM method by Baid Sokayna, Hilali Youssef, Mesmoudi Saïd, Bourihane Oussama

“…The governing partial differential equations are discretized using the Galerkin method and solved by combining a Taylor series expansion with a continuation procedure. …”
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