Identification of the boundary regime in the process of water-oil displacement from the reservoir by Gamzaev Khanlar

“…The water-oil displacement process (from a rectangular reservoir) has been considered, that is described by a nonlinear system of partial differential equations with respect to the reservoir pressure (RP) and displacing phase saturation (DPS). …”
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Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension by E. Navarro, L. Jódar, R. Company

“…In this paper, we develop a Frobenius matrix method for solving higher order systems of differential equations of the Fuchs type. Generalized power series solution of the problem are constructed without increasing the problem dimension. …”
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Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy by Chao Yue, Tiecheng Xia

“…Then, the CCIRD equations are decomposed into Dubrovin-type ordinary differential equations. Furthermore, the theory of the trigonal curve and the properties of the three kinds of Abel differentials are applied to obtain the explicit theta function representations of the Baker-Akhiezer function and the meromorphic functions. …”
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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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Application of Local Fractional Homotopy Perturbation Method in Physical Problems by Nabard Habibi, Zohre Nouri

“…Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. …”
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Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument by Kuo-Shou Chiu

“…Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. …”
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On fractional Pennes bio-heat equation using Legendre collocation method by Arvind Kumar Mishra, Sushil Kumar, Ajay Kumar Shukla

“…The best feature of the proposed technique is the conversion of fractional-order differential equations into a set of algebraic systems and the ability to approximate both spatial and temporal coordinates with a single basis. …”
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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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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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Analytic Solutions of Some Self-Adjoint Equations by Using Variable Change Method and Its Applications by Mehdi Delkhosh, Mohammad Delkhosh

“…Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011). …”
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A Novel Method for Constructing Grid Multi-Wing Butterfly Chaotic Attractors via Nonlinear Coupling Control by Yun Huang

“…Based on the three-dimensional Lorenz system, two first-order differential equations are added along with one linear coupling controller, respectively. …”
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Solving arbitrary one-loop reduction via generating function by Tingfei Li, Yuekai Song, Liang Zhang

“…We first establish the partial differential equations governing the higher-pole generating function. …”
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Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method by E. H. Doha, W. M. Abd-Elhameed

“…The proposed algorithms are extended to solve the two-dimensional sixth-order differential equations. A family of symmetric generalized Jacobi polynomials is introduced and used as basic functions. …”
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Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation by Naveed Iqbal, Azmat Ullah Khan Niazi, Ramsha Shafqat, Shamsullah Zaland

“…With the help of few conditions on functions P:I×E1×E1⟶E1, WI is control and it belongs to E1, A∈FI,LE1, and α stands for the highly continuous fuzzy differential equation generator. Finally, a few instances of fuzzy fractional differential equations are shown.…”
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Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation by Mehmet Emir Koksal

“…Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. …”
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Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function by David W. Pravica, Njinasoa Randriampiry, Michael J. Spurr

“…They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the recursion relations and ODEs satisfied by the nth degree Legendre polynomials. …”
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Optimal control of vaccine distribution in a rabies metapopulation model by Erika Asano, Louis J. Gross, Suzanne Lenhart, Leslie A. Real

“…This system of ordinary differential equations considers subpop-ulations connected by movement. …”
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Investigation of a spatial double pendulum: an engineering approach by S. Bendersky, B. Sandler

“…Matlab computer programs were used for solving the nonlinear differential equations by the Runge-Kutta method. Fourier transformation was used to obtain the frequency spectra for analyses of the oscillations of the two pendulums. …”
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Positive Position Feedback Control for High-Amplitude Vibration of a Flexible Beam to a Principal Resonance Excitation by Li Jun

“…The perturbation method of multiple scales is employed to find the general nonlinear response of the system and four first-order differential equations governing the amplitudes and phases of the responses are derived. …”
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The Dynamical Behavior of a Rigid Body Relative Equilibrium Position by T. S. Amer

“…The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. …”
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