Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes by A. R. Appadu

“…Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. …”
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Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices by Xiongfei Zou, Ying Tang, Shirong Bu, Zhengxiang Luo, Shouming Zhong

“…Although the ordinary differential equation on which our proposed algorithm is built is only n-dimensional, it can succeed to extract n-dimensional complex eigenvectors that are indeed 2n-dimensional real vectors. …”
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A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem by Marcelo Franco de Oliveira, Daniele Cristina Thoaldo, Rodrigo Dias

“…In this approach, a weighting function with respect to time is used in the fundamental differential equation. By assuming a linear variation in some time interval, a time integration is performed. …”
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A New Way to Generate an Exponential Finite Difference Scheme for 2D Convection-Diffusion Equations by Caihua Wang

“…The idea of the method can be applied to a wide variety of differential equations.…”
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Experimental Validation of Elliptical Fin-Opening Behavior by James M. Garner, Paul Weinacht, Robert P. Kaste

“…A second order differential equation was used to model elliptical fin deployment history and accounts for: deployment with respect to the geometric properties of the fin, the variation in fin aerodynamics during deployment, the initial yaw effect on fin opening, and the variation in deployment speed based on changes in projectile spin. …”
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Variational analysis for simulating free-surface flows in a porous medium by Shabbir Ahmed, Charles Collins

“…A variational formulation has been developed to solve a parabolic partial differential equation describing free-surface flows in a porous medium. …”
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New Numerical Solution of von Karman Equation of Lengthwise Rolling by Rudolf Pernis, Tibor Kvackaj

“…The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. …”
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Magnetoelastic Principal Parametric Resonance of a Rotating Electroconductive Circular Plate by Zhe Li, Yu-da Hu, Jing Li

“…The axisymmetric parameter vibration differential equation of the variable-velocity rotating circular plate is obtained through the application of Galerkin integral method. …”
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Study on Galloping Oscillation of Iced Catenary System under Cross Winds by Guo Chen, Yiren Yang, Yang Yang, Peng Li

“…The partial differential vibration equation of the system is converted into the ordinary differential equation by the Galerkin method and then numerically solved. …”
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Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation by Tahir Ayaz, Farhad Ali, Wali Khan Mashwani, Israr Ali Khan, Zabidin Salleh, Ikramullah

“…The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. …”
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Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment by Bing Liu, Shi Luan, Yinghui Gao

“…In this paper, based on impulsive differential equation, the dynamics of a single-species model with impulsive pollution treatment at fixed time in a polluted environment is considered, in which we assume that the species is directly affected by the pollutants. …”
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Laminar Motion of the Incompressible Fluids in Self-Acting Thrust Bearings with Spiral Grooves by Cornel Velescu, Nicolae Calin Popa

“…Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the “pumping” direction. …”
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Analytical Method for Capped Pile–Soil Interaction considering the Load Action of Soil under the Pile Cap by Shilin Luo, Mingquan Liu, Jianqing Jiang, Ailifeila Aierken, Jin Chang, Xuewen Zhang, Rui Zhang

“…The theoretical expressions of axial force and load-settlement curves are also achieved by means of establishing and solving the equilibrium differential equation of the pile body. Comparison of calculation results with the ordinary pile indicates that soil load under the pile cap reduces the lateral friction value; the influenced depth is about four times of the load action radius. …”
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Study on dynamics characteristic on combination misalignment and rubbing of the dual-rotor system by YAO Xia, NAN Guofang, LI Yao, QIU Xuewen

“…The misalignment of the dual-rotor system for the aero-engine will lead to abnormal increase of the vibration which results in the rotor-stator rubbing and affects the safty and stability of the rotor operation.The dual-rotor system was taken as the research object.Considering the combination misalignment-rubbing fault, the dynamic model of the rotor system is established based on the lumped mass method.The differential equation of the system motion was established according to the Lagrange equation, and the Range-Kutta method was used to solve it.The influence mechanism of the key parameters such as the speed, the misalignment angle and the coupling misalignment on the nonlinear dynamic characteristics of the system was studied.The results show that the system presents complex dynamic characteristics such as periodic, multi-periodic, quasi-periodic and chaotic motion with the increase of the rotor’s speed.When the speed is in the range of 1 500-2 200 rad/s, the system switches between periodic 2 motion and chaotic state through multiple paroxysmal bifurcations and paroxysmal inverted bifurcations.There are nonlinear phenomena such as jump in the bifurcation diagram of the vibration response with the change of the parallel misalignment of the coupling.As the misalignment angle of the bearing increases, the chaotic interval of the high speed decreases, and the stable periodic motion interval increases.…”
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Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model by Congyin Fan, Kaili Xiang, Peimin Chen

“…Further, the partial differential equation (PDE) for the prices of European call option is derived by using risk neutral pricing principle and the numerical solution of the PDE is calculated by the Crank-Nicolson scheme. …”
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A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method by Hamzeh Zureigat, Mohammad A. Tashtoush, Ali F. Al Jassar, Emad A. Az-Zo’bi, Mohammad W. Alomari

“…This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. …”
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An Improved Finite Difference Type Numerical Method for Structural Dynamic Analysis by Sung-Hoon Kim, Youn-sik Park

“…An improved finite difference type numerical method to solve partial differential equations for one-dimensional (1-D) structure is proposed. …”
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The effects of heterogeneity on Darcy-Benard convection saturated with a ferrofluid by Moussa Rachida, Lagziri Hajar, El Khanoussi Fadoua, El Fakiri Hanae

“…A dimensionless formulation and linear stability analysis are employed to derive an ordinary differential equation, which is solved using the shooting method and a Runge-Kuttasolver. …”
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Parametric Study on the Influence of Warping Deformation upon Natural Frequencies of Die Springs by Ying Hao, Junfeng Guan

“…The warping deformation of spring’s cross section, as a new design factor, is incorporated into the differential equation of motion. Numerical simulations show that the warping deformation is a significant role of the behavior of natural frequencies of die springs and should be considered carefully. …”
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A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet by Sachin Kumar, Jinde Cao, Xiaodi Li

“…In this research work, we focused on finding the numerical solution of time-fractional reaction-diffusion and another class of integro-differential equation known as the integro reaction-diffusion equation. …”
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