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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DYNAMICS CHARACTERISTICS AND EXPERIMENTAL ANALYSIS ON THE OBLIQUE CUTTING OF PLOW SYSTEM by ZHANG Yu, CHEN HongYue, HAO ZhiYong, MAO Jun

“…Aiming at the mechanical properties of plow head and dynamic charateristics of system under oblique cutting condition,cutting resistance of planning tool under oblique cutting condition was derived,and was treated as external excitation. Dynamic differential equation of plow system were established by using the finite element method,and were solved by using numerical method. …”
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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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IMPROVED FINITE ELEMENT TRANSFER MATRIX METHOD OF PLANE BEAM ELEMENTS USING THE ABSOLUTE NODAL COORDINATE FORMULATION by QIAN ShuangLin, HE Bin, YAO LiKe, NI ChunHai, LV JianDong

“…Here ordinary differential equation numerical methods can be applied conveniently. …”
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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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On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations by Said Mesloub

“…This paper is devoted to the study of the well-posedness of an initial boundary value problem for an odd higher order nonlinear pseudohyperbolic integrodifferential partial differential equation. We associate to the equation n nonlocal conditions and n+1 classical conditions. …”
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Spectral Differentiation and Mimetic Methods for Solving the Scalar Burger’s Equation by Bertha K. Rodriguez-Chavez, Yessica E. Zarate-Pedrera

“…In the present work, the spectral differentiation method was studied to solve the scalar Burger’s partial differential equation. This equation has been of considerable physical interest as it can be regarded as a simplified version of the Navier-Stokes equations. …”
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Preliminary analysis of an agent-based model for a tick-borne disease by Holly Gaff

“…The results from this model arecompared with those from previously published differential equation based populationmodels. The findings show that the agent-based model produces significantly lower prevalenceof disease in both the ticks and their hosts than what is predicted by a similardifferential equation model.…”
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Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments by S. Shao, C. L. Chang

“…After defining the process of conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient of the convection term. …”
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Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks by Huitao Zhao, Yaowei Sun, Zhen Wang

“…A delayed Lotka-Volterra predator-prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard’s method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. …”
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A model of regulatory dynamics with threshold-type state-dependent delay by Qingwen Hu

“…A general model which is an extension of the classical differential equation models with constant or zero time delays is developed to study the stability of steady state, the occurrence and stability of periodic oscillations in regulatory dynamics. …”
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Vibration Suppression of a Coupled Aircraft Wing with Finite-Time Convergence by Yiming Liu, Zhifeng Tan, Xiaofen Yang, Xiaowei Wang

“…Since the model is modeled by partial differential equations, the traditional control design scheme based on the ordinary differential equation model is not applicable, and the control law design becomes very complex. …”
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