Analytical Method in Solving Flow of Viscoelastic Fluid in a Porous Converging Channel by M. Esmaeilpour, Naeem Roshan, Negar Roshan, D. D. Ganji

“…An analytical method, called homotopy perturbation method (HPM), is used to compute an approximation to the solution of the nonlinear differential equation governing the problem of two-dimensional and steady flow of a second-grade fluid in a converging channel. …”
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Taking into account the lens geometric distortion during accumulation of blurred star images in an astro-inertial attitude sensor by S. N. Vasilyuk

“…The analytical approach uses a model of direct distortion correction, which makes it possible to obtain a new differential equation for the blur trajectory in the image plane with distortion. …”
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Convergence Time Calculation for Supertwisting Algorithm and Application for Nonaffine Nonlinear Systems by Jianhua Zhang, Quanmin Zhu, Yang Li

“…The convergence time of the STA is provided by calculating the solution of a differential equation instead of constructing Lyapunov function. …”
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Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input by Bing Liu, Ling Xu, Baolin Kang

“…By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. …”
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Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators by Luciano Abadias, Pedro J. Miana

“…In this paper we treat the following partial differential equation, the quasigeostrophic equation: ∂/∂t+u·∇f=-σ-Aαf,  0≤α≤1, where (A,D(A)) is the infinitesimal generator of a convolution C0-semigroup of positive kernel on Lp(Rn), with 1≤p<∞. …”
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Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem by Wen Lian, Zhanbing Bai

“…The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0,   0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3,  CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. …”
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Positive Solutions for the Initial Value Problems of Fractional Evolution Equation by Yue Liang, Yu Ma, Xiaoyan Gao

“…As an example, we study the partial differential equation of parabolic type of fractional order.…”
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A Class of PDEs with Nonlinear Superposition Principles by Li Peng, Liu Keying, Pan Zuliang, Zhong Weizhou

“…In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.…”
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Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations by Zeid I. A. Al-Muhiameed, Emad A.-B. Abdel-Salam

“…With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. …”
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The Telegraph Equation and Its Solution by Reduced Differential Transform Method by Vineet K. Srivastava, Mukesh K. Awasthi, R. K. Chaurasia, M. Tamsir

“…Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. …”
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Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales by Quanwen Lin, Baoguo Jia, Qiru Wang

“…As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ([x′(t)]α)′+csintxα(t)=cos⁡t, where α=p/q, p, q are odd positive integers.…”
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Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility by Min-Ku Lee, Jeong-Hoon Kim, Kyu-Hwan Jang

“…The multiscale partial differential equation for the option price is approximated by a couple of single scale partial differential equations. …”
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Analytic Approximate Solution for Falkner-Skan Equation by Vasile Marinca, Remus-Daniel Ene, Bogdan Marinca

“…This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. …”
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Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form by Abdelrady Okasha Elnady, M. Fayek Abd Rabbo, Hani M. Negm

“…A numerical method for the solution of the Falkner–Skan equation, which is a nonlinear differential equation, is presented. The method has been derived by truncating the semi-infinite domain of the problem to a finite domain and then expanding the required approximate solution as the elements of the Chebyshev series. …”
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Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme by Muhammad Nadeem, Hanan A. Wahash

“…The fractional differential equation may be transformed into its partner equation using He’s fractional complex transform, and then, the nonlinear elements can be readily handled using the homotopy perturbation method (HPM). …”
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Determination of the response of a class of nonlinear time invariant systems by Sudhangshu B. Karmakar

“…The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first obtained in terms of the input in the form of a Volterra functional expansion. …”
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Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation by Mohammad Mehdizadeh Khalsaraei, Ali Shokri, Zahra Mohammadnia, Hamid Mohammad Sedighi

“…In this paper, we use a numerical method for solving the nonlinear Black–Scholes partial differential equation of the European option under transaction costs, which is based on the nonstandard discretization of the spatial derivatives. …”
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A Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEs by I. B. Aiguobasimwin, R. I. Okuonghae

“…In this paper, a new class of two-derivative two-step Runge-Kutta (TDTSRK) methods for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equation (ODEs) is considered. The TDTSRK methods are a special case of multi-derivative Runge-Kutta methods proposed by Kastlunger and Wanner (1972). …”
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Dynamical Analysis of a Pest Management Model with Saturated Growth Rate and State Dependent Impulsive Effects by Wencai Zhao, Tongqian Zhang, Xinzhu Meng, Yang Yang

“…Secondly, by using geometry theory of impulsive differential equation, the existence and stability of periodic solution of the system are discussed. …”
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The stability of collocation methods for VIDEs of second order by Edris Rawashdeh, Dave McDowell, Leela Rakesh

“…Simplest results presented here are the stability criteria of collocation methods for the second-order Volterra integro differential equation (VIDE) by polynomial spline functions. …”
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