Application of PDE Constrained Optimization in Internal Combustion Engine Pollution Control by Hongliang Guan

“…Aiming at the problem of secondary pollution of waters due to the difficulty of controlling the dosage of purifiers in the treatment of internal combustion engine pollution, a partial differential equation (referred to as PDE) constrained optimization algorithm based on l1-norm is proposed. …”
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Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction by Weili Kong, Yuanfu Shao

“…Secondly, by comparison theory of the stochastic differential equation, we study the extinction and permanence in the mean of all species. …”
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On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise in ℝd by Xichao Sun, Zhi Wang, Jing Cui

“…We study a stochastic partial differential equation in the whole space x∈ℝd, with arbitrary dimension d≥1, driven by fractional noise and a pure jump Lévy space-time white noise. …”
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Reducing the sign problem with line integrals by Rasmus N. Larsen

“…We lay out how to write down an ordinary differential equation for the line integrals. As an example of its usage, we apply the results to a 1d quantum mechanical anharmonic oscillator with a x 4 potential in real time, finite temperature.…”
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The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems by Yanling Shi, Jia Li

“…We study the following two-order differential equation, (Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0, where Φp(s)=|s|(p-2)s, p>0. f(x,t) and g(x,t) are real analytic functions in x and t, 2aπp- periodic in x, and quasi-periodic in t with frequencies (ω1,…,ωm). …”
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The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact by Zhi-Long He, Lin-Fei Nie

“…By using the geometry theory of differential equation and method of successor function, the existence of positive order-1 periodic solution is studied. …”
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The traveling wave solution and dynamics analysis of the fractional order generalized Pochhammer–Chree equation by Chunyan Liu

“…First, the fractional order generalized Pochhammer–Chree equation is transformed into an ordinary differential equation. Second, the dynamic behavior is analyzed using the planar dynamical system, and some three-dimensional and two-dimensional phase portraits are drawn using Maple software to reflect its chaotic behaviors. …”
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Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term by Rui Cao

“…A nonlinear Schrödinger equation with a higher-order dispersive term describing the propagation of ultrashort femtosecond pulses in optical fibres is considered and is transformed into a second-order nonlinear ordinary differential equation. We investigate the exact travelling wave solutions of the nonlinear Schrödinger equation using three methods, namely, the auxiliary equation method, the first integral method, and the direct integral method. …”
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Double Periodic Wave Solutions of the (2 + 1)-Dimensional Sawada-Kotera Equation by Zhonglong Zhao, Yufeng Zhang, Tiecheng Xia

“…Based on a general Riemann theta function and Hirota’s bilinear forms, we devise a straightforward way to explicitly construct double periodic wave solution of (2+1)-dimensional nonlinear partial differential equation. The resulting theory is applied to the (2+1)-dimensional Sawada-Kotera equation, thereby yielding its double periodic wave solutions. …”
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A Numerical Method for Computing the Principal Square Root of a Matrix by F. Soleymani, S. Shateyi, F. Khaksar Haghani

“…Finally, application of the presented approach is illustrated in solving a matrix differential equation.…”
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Comparison of Analytical Solution of DGLAP Equations for... by Neelakshi N. K. Borah, D. K. Choudhury, P. K. Sahariah

“…The DGLAP equation for the nonsinglet structure function F 2 N S ( x , t ) at LO is solved analytically at low x by converting it into a partial differential equation in two variables: Bjorken x and t    ( t = l n ( Q 2 / Λ 2 ) and then solved by two methods: Lagrange’s auxiliary method and the method of characteristics. …”
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Computational Modelling of Thermal Stability in a Reactive Slab with Reactant Consumption by O. D. Makinde

“…The nonlinear partial differential equation governing the transient reaction-diffusion problem is solved numerically using a semidiscretization finite difference technique. …”
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Mathematical Modeling of the Transmission Dynamics of Gumboro Disease by J. S. Musaili, I. Chepkwony, W. N. Mutuku

“…The basic reproduction number Rog is derived, and the dynamical behaviors of both the disease-free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever Rog<1 and an asymptotic stable EE whenever Rog>1. …”
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Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel by Jawad Raza, Azizah Mohd Rohni, Zurni Omar

“…Governing partial differential equation of the proposed problem converted into nonlinear ordinary differential equations by using similarity transformation. …”
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Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods by Arzu Akbulut

“…Thus, using the suitable wave transform, the given equation is converted into an ordinary differential equation. Then, the proposed methods are applied to the reduced equation. …”
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Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population by Leonid Shaikhet

“…A necessary and sufficient condition for asymptotic mean square stability of the equilibrium point of the linear part of the considered stochastic differential equation is obtained. This condition is at the same time a sufficient one for stability in probability of the equilibrium point of the initial nonlinear equation. …”
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Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates by Saeed Dinarvand, Abed Moradi

“…The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). …”
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Identification of a Stochastic Dynamic Model for Aircraft Flight Attitude Based on Measured Data by Haiquan Li, Xiaoqian Chen, Jiatu Zhang, Bochen Wang, Jiahui Peng, Liang Wang

“…Therefore, a stochastic differential equation for aircraft flight attitude is modeled based on the traditional one in this paper. …”
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Disease dynamics for the hometown of migrant workers by Ram P. Sigdel, C. Connell McCluskey

“…Biol. 300:100--109 (2012) formulatedand studied a delay differential equation model for disease dynamics in a region where a portionof the population leaves to work in a different region for an extended fixed period. …”
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A Simple Distributed RGC Model of MOSFET for Pre-Pinch Off Region by Umesh Kumar, Arun Mirchandani

“…The differential equation describing the small signal behavior of a MOSFET channel is derived. …”
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