Buckling of Euler Columns with a Continuous Elastic Restraint via Homotopy Analysis Method by Aytekin Eryılmaz, M. Tarık Atay, Safa B. Coşkun, Musa Başbük

“…HAM has been successfully applied to many linear and nonlinear, ordinary and partial, differential equations, integral equations, and difference equations. …”
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Analysis of Magnetohydrodynamic Micropolar Nanofluid Flow due to Radially Stretchable Rotating Disk Employing Spectral Method by Ayele Tulu

“…To begin with, the model is developed in the form of nonlinear partial differential equations (PDEs) for momentum, microrotation, thermal, and concentration with their boundary conditions. …”
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Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn by Muhammad Shakeel, Naseem Abbas, Muhammad Junaid U. Rehman, Fehaid Salem Alshammari, Abdullah Al-Yaari

“…Using a transformation method, the nonlinear partial differential equations (NPDEs) are converted into various nonlinear ordinary differential equations (NLODEs), providing the numerous closed-form solitary wave solutions. …”
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Fractional Modeling of Non-Newtonian Casson Fluid between Two Parallel Plates by Mubashir Qayyum, Sidra Afzal, Efaza Ahmad

“…The Casson fluid model is fractionally transformed through mixed similarity transformations. As a result, partial differential equations (PDEs) are transformed to a fractional ordinary differential equation (FODE). …”
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MHD Flow and Heat Transfer between Coaxial Rotating Stretchable Disks in a Thermally Stratified Medium. by Tasawar Hayat, Sumaira Qayyum, Maria Imtiaz, Ahmed Alsaedi

“…We convert system of partial differential equations into system of highly nonlinear ordinary differential equations after employing the suitable transformations. …”
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Unsteady Stagnation Point Flow and Heat Transfer over a Stretching/Shrinking Sheet with Suction or Injection by M. Suali, N. M. A. Nik Long, N. M. Ariffin

“…The unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction/injection is studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using a similarity transformation and solved numerically. …”
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Approximate Analytical Study of Time-Dependent MHD Casson Hybrid Nanofluid over a Stretching Sheet and Considering Thermal Radiation by Ali Rehman, Zabidin Salleh, Abd Allah A. Mousa, Ebenezer Bonyah, Waris Khan

“…The novelty of present research is that the first time-dependent Casson MHD flow of hybrid is addressed analytically in the form of a series solution along with flexible properties on an extending surface. Transforming the nonlinear partial differential equation to nonlinear ordinary differential equation, we used the defined similarity transformation. …”
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Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems by S. S. Motsa, P. G. Dlamini, M. Khumalo

“…Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). …”
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Algorithms for Solving the Equilibrium Composition Model of Arc Plasma by Zhongyuan Chi, Yuzhang Ji, Ningning Liu, Tianchi Jiang, Xin Liu, Weijun Zhang

“…The model was formulated on the basis of the Saha and Guldberg–Waage equations, integrated with Dalton’s law of partial pressures, stoichiometric equilibrium, and the law of conservation of charge, resulting in a nonlinear system of equations with a weakly singular Jacobian matrix. …”
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Peristaltic Transport of a Jeffrey Fluid with Variable Viscosity through a Porous Medium in an Asymmetric Channel by A. Afsar Khan, R. Ellahi, K. Vafai

“…The channel asymmetric is produced by choosing the peristaltic wave train on the wall of different amplitude and phase. The governing nonlinear partial differential equations for the Jeffrey fluid model are derived in Cartesian coordinates system. …”
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Effect of Internal Heat Generation/Absorption on Dusty Fluid Flow over an Exponentially Stretching Sheet with Viscous Dissipation by G. M. Pavithra, B. J. Gireesha

“…A numerical analysis has been carried out to describe the boundary layer flow and heat transfer of a dusty fluid over an exponentially stretching surface in the presence of viscous dissipation and internal heat generation/absorption. The governing partial differential equations are reduced to nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by Runge-Kutta-Fehlberg 45 method. …”
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Modeling and Numerical Simulation of Semitensioned Mooring Line under Taut-Slack State by Ruizhi Shi, Suxia Zhang, Xijun Liu, Chong Tian

“…Directly using the finite difference method for numerically solving partial differential equations of mooring line, the dynamic responses can be obtained. …”
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Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods by Norhasimah Mahiddin, S. A. Hashim Ali

“…The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. …”
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Modelling Water Waves on Graphs by André Nachbin

“…Water waves are a good topic for comparing different mathematical models, from hyperbolic conservation laws to weakly nonlinear, weakly dispersive systems of partial differential equations on a two-dimensional fattened (thick) graph and the respective one-dimensional graph-model reduction. …”
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Faber-Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions Cost by Shu-Li Mei

“…The operator can be used to discretize the weak solution function of the nonlinear second-order PDEs. Second, using the couple technique of the variational iteration method (VIM) and the precision integration method, the sparse approximation solution of the nonlinear partial differential equations can be obtained. …”
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Dual Solutions and Stability Analysis of Cu-H2O-Casson Nanofluid Convection past a Heated Stretching/Shrinking Slippery Sheet in a Porous Medium by Kifle Adula Duguma, Oluwole Daniel Makinde, Lemi Guta Enyadene

“…Using some realistic assumptions and appropriate similarity transformations, the governing nonlinear partial differential equations were formulated and transformed into a system of nonlinear ordinary differential equations and then numerically solved by using the shooting technique. …”
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Numerical Investigation of the Finite Thin Film Flow for Hybrid Nanofluid with Kerosene Oil as Base Fluid over a Stretching Surface along with the Viscous Dissipation and Variable... by Yasir Mehmood, Ammar Alsinai, Ramsha Shafqat, Muhammad Bilal, Allah Yar Khan, Read S. A. Qahtan

“…To study the phenomenon of thermal conduction, a modified version of Fourier’s law model is adopted because in the power-law model, the thermal conductivity depends on the velocity gradient. A system of nonlinear ordinary differential equations is obtained by considering the similarity transformations over the obtained rheological system of partial differential equations which is then tackled by a well-known numerical approach, i.e., the bvp4c MATLAB technique. …”
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NANOFLUID FLOW ON A VERTICAL CYLINDER UNDER THE EFFECT OF MAGNETOHYDRODYNAMICS by Manal H. Saleh

“…These equations are transformed to dimensionless equations using vorticity-stream function method and the resulting nonlinear system of partial differential equations are then solved numerically using finite difference approximation. …”
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Natural Convection Flow on a Vertical Cylinder with Sinusoidal Temperature Oscillation Under The Effect of Magneto Hydrodynamic by Manal H. AL-Hafidh

“…These equations are transformed to dimensionless equations using vortices-stream function method and the resulting nonlinear system of partial differential equations are then solved numerically using finite difference approximation. …”
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Exploring chaos and sensitivity in the Ivancevic option pricing model through perturbation analysis. by Adil Jhangeer, Ali R Ansari, Ariana Abdul Rahimzai, Beenish, Abdul Qadeer Khan

“…This study explores the Ivancevic Option Pricing Model, a nonlinear wave-based alternative to the Black-Scholes model, using adaptive nonlinear Schrödingerr equations to describe the option-pricing wave function influenced by stock price and time. …”
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