Third-Order Approximate Solution of Chemical Reaction-Diffusion Brusselator System Using Optimal Homotopy Asymptotic Method by Salem Alkhalaf

“…It is observed that the method is easy to implement and quite valuable for handling nonlinear system of partial differential equations and yielding excellent results at minimum computational cost. …”
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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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Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications by Veli Shakhmurov

“…The infinite systems of the degenerate partial differential equations and Cauchy problem for system of parabolic equations are further studied in applications.…”
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Quasilinear Hyperbolic Systems Applied to Describe the Magnetohydrodynamic Nanofluid Flow by Dayong Nie

“…The influence of velocity slip on the flow and heat transfer properties of a hyperbolic nanofluid has been investigated. The partial differential equations for nanoparticle solid concentration, energy, and motion were turned into ordinary differential equations. …”
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Periodic Problems of Difference Equations and Ergodic Theory by B. A. Biletskyi, A. A. Boichuk, A. A. Pokutnyi

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Monotonic Limit Properties for Solutions of BSDEs with Continuous Coefficients by ShengJun Fan, Xing Song, Ming Ma

“…This paper investigates the monotonic limit properties for the minimal and maximal solutions of certain one-dimensional backward stochastic differential equations with continuous coefficients.…”
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Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme by Zhaofeng An, Suxia Zhang, Jinhu Xu

“…In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. …”
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Travelling wave solutions to some PDEs of mathematical physics by Kourosh Nozari, Ghasem Alizadeh Afrouzi

“…As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity and multifluid flows, or some new cosmological models such as signature changing space-times. …”
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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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Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency by Rodrigue Yves M’pika Massoukou, Suares Clovis Oukouomi Noutchie, Richard Guiem

“…The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. …”
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On expansions for nonlinear systems Error estimates and convergence issues by Beauchard, Karine, Le Borgne, Jérémy, Marbach, Frédéric

“…Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. …”
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ESTABLISHED MODES AND STATIC CHARACTERISTICS OF THREE-PHASE ASYNCHRONOUS MOTOR POWERED WITH SINGLE PHASE NETWORK by V. S. Malyar, V. V. Malyar

“…In order to perform it, the original nonlinear differential equations are algebraized by approximating the variables with the use of cubic splines. …”
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Some Relations between Certain Complex Equations and Nonnormalized Meromorphic Functions by Hüseyin Irmak

“…The purpose of this investigation is first to reveal some relations between certain complex (differential) equations and nonnormalized meromorphic functions and then to point some of their useful consequences out.…”
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The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative by Chun-Guang Zhao, Ai-Min Yang, Hossein Jafari, Ahmad Haghbin

“…Analytical solutions for the homogeneous and nonhomogeneous local fractional differential equations are discussed by using the Yang-Laplace transform.…”
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Solutions of type rm for a class of singular equations by Abdullah Altin

“…We obtain all solutions of radial type for a class of singular partial differential equations of even order. The essential operators here are elliptic or ultrahyperbolic.…”
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Existence of Positive Solutions for a Functional Fractional Boundary Value Problem by Chuanzhi Bai

“…We study the existence of positive solutions for a boundary value problem of fractional-order functional differential equations. Several new existence results are obtained.…”
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Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling by O. D. Makinde, S. Khamis, M. S. Tshehla, O. Franks

“…The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. …”
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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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Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink by I. Swain, S. R. Mishra, H. B. Pattanayak

“…The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. …”
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