Substantiation of asymptotical solution of weakly nonlinear hyperbolic system by Aleksandras Krylovas

“… A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. …”
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An Iterative Method for Time-Fractional Swift-Hohenberg Equation by Wenjin Li, Yanni Pang

“…Using this iterative method, we obtain the approximate analytic solutions with numerical figures to initial value problems, which indicates that such iterative method is effective and simple in constructing approximate solutions to Cauchy problems of time-fractional differential equations.…”
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The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion by Zulqurnain Sabir, Assad Ayub, Juan L. G. Guirao, Saira Bhatti, Syed Zahir Hussain Shah

“…The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. …”
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Analytical study of steady state axisymmetric stagnation-point gold–blood Casson nanofluid through a rotating stretchable disk by Usman Ali, Hamid Khan, Waris Khan, Emad E. Mahmoud, Marouan Kouki, Jabr Aljedani, Hakim AL Garalleh

“…By using scaling variables, the complex system of partial differential equations is simplified into a set of coupled high degree nonlinear ordinary differential equations with convective boundary conditions. …”
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The significance of magnetized thermal radiation on the magnetohydrodynamic (MHD) behavior of Williamson hybrid ferrofluids over a stretching sheet by D. Thenmozhi, M. Eswara Rao, P.D. Selvi, RLV. Renuka Devi, S. Kiranmaiye, Ch. Nagalakshmi

“…The study is mathematically modeled using partial differential equations (PDEs) accounting for the deformation vortices of a stretching surface. …”
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Computational analysis of bioconvective MHD hybrid nanofluid flow of non-Newtonian fluid over cone/plate: A study based on the Cattaneo-Christov heat and mass flux model by P. Francis, P. Sambath, S. Noeiaghdam, U. Fernandez-Gamiz, S. Dinarvand

“…A similarity transformation is used to simplify the complex partial differential equations into ordinary differential equations, which are then solved using the Keller Box finite difference method. …”
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Thermodynamics and solar radiative analysis in Jeffery-Hamel flow through non-parallel channel by novel improved residual power series method by Mohamed Bouzidi, Mohsin Ul Haq, Ikram Ullah, Saira Shukat, Hijaz Ahmad, Mohammad Mahtab Alam, Hamid Khan, Marouan Kouki

“…The governing system of partial differential equations can be transformed into ordinary differential equations (ODEs) using suitable transformations. …”
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Application of DTM to heat source/sink in squeezing flow of iron oxide polymer nanofluid between electromagnetic surfaces by Reshu Gupta, A.B. Albidah, NFM Noor, Ilyas Khan

“…The governing partial differential equations (PDEs) for flow, heat, and mass transfer are transformed into nonlinear ordinary differential equations (ODEs) through the appropriate similarity transformation. …”
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A comprehensive numerical study exploring the significance of thermally reactive bioconvection in Falkner-Skan flow of Williamson nanomaterials influenced by activation energy and... by M. Israr Ur Rehman, Haibo Chen, Aamir Hamid, Wu Qian, Refka Ghodhbani, Mohamed Hussien

“…Similarity transformations are used to convert the system of partial differential equations into a system of ordinary differential equations, which are then numerically solved using the Runge–Kutta–Fehlberg (RKF-45) method. …”
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Numerical Solution of Binary Liquid-Phase Adsorption onto Porocel Clay Using Linear, Freundlich and Langmuir Isotherms by Olaosebikan A. Olafadehan, Alfred A. Susu

“…The scheme is based on orthogonal collocation for spatial discretization of the resulting set of coupled hyperbolic and parabolic partial differential equations for the macro-and micro-system, respectively. …”
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Computational analysis of EMHD nanofluid flow over a thermally conductive surface: Enhancing heat transfer for industrial applications by Faiza Zahid, Muhammad Bilal Riaz

“…The problem under scrutiny yields a non-similar solution necessitating the transformation of governing partial differential equations into ordinary differential equations by the use of similarity variables. …”
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Mathematical modeling of velocity and accelerations fields of image motion in the optical equipment of the Earth remote sensing satellite by S. Yu. Gorchakov

“…For modeling the orbital and angular motion of the satellite, differential equations with numerical integration were used. …”
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Analytical Investigation of Laminar Viscoelastic Fluid Flow over a Wedge in the Presence of Buoyancy Force Effects by B. Rostami, M. M. Rashidi, P. Rostami, E. Momoniat, N. Freidoonimehr

“…The two-dimensional boundary-layer governing partial differential equations (PDEs) are derived by the consideration of Boussinesq approximation. …”
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Nonlinear Vibration Analysis for Stiffened Cylindrical Shells Subjected to Electromagnetic Environment by Xue-Qin Li, Guang-Chen Bai, Lu-Kai Song, Wei Zhang

“…By employing the Galerkin discretization procedure, the partial differential equations are diverted to a set of coupled nonlinear ordinary differential equations of motion. …”
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Theoretical and numerical study of profit in agricultural sector model using wavelet method by Yeshwanth R., Kumbinarasaiah S.

“…The operational matrices are used to simplify fractional differential equations to an algebraic system of equations. …”
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Irreversibility and Sensitivity analysis of MHD squeezing various shaped nanofluid flow between parallel permeable disks by Abdul Awal, Md. Sarwar Alam

“…The system of partial differential equations governing the flow is converted to a coupled of non-dimension ordinary differential equations. …”
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Analysis of the Three-Dimensional Dynamic Problems by Using a New Numerical Method by Yao Rong, Yang Sun, LiQing Zhu, Xiao Xiao

“…In this paper, the scaled boundary element method (SBFEM) is used to analyze the displacement and pore pressure response of saturated soil due to consolidation under dynamic load. The partial differential equations of linear problems are transformed into ordinary differential equations and solved along the radial direction. …”
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Nonstationary Fronts in the Singularly Perturbed Power-Society Model by M. G. Dmitriev, A. A. Pavlov, A. P. Petrov

“…The theory of contrasting structures in singularly perturbed boundary problems for nonlinear parabolic partial differential equations is applied to the research of formation of steady state distributions of power within the nonlinear “power-society” model. …”
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Existence Results for an Implicit Coupled System Involving $\xi$-Caputo and $p$-Laplacian Operators by Walid Benhadda, Abderrazak Kassidi, Ali El Mfadel, Elomari M'hamed

“…This paper aims to establish the existence and uniqueness of a solution to a coupled system of $\xi$-Caputo fractional differential equations involving the $p$-Laplacian operator in an arbitrary Banach space. …”
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Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media by Ivan Tsyfra, Tomasz Czyżycki

“…The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.…”
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