RESEARCH ON NONLINEAR VIBRATION FOR ELECTRICALLY ACTUATED SINGLE-WALLED CARBON NANOTUBE by YANG ZhiAn, LIU ZhiWei

“…According to the beam theory,the nonlinear dynamic equation of carbon nanotube system is established,it is a nonlinear partial differential equation. By means of the method of multiple scales,nonlinear vibration equation of the system is acquired and the numerical calculation is carried out. …”
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Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process by Hao Chang, Xi-min Rong

“…Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. …”
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Asymptotic Behavior of an Optimal Investment-Reinsurance Problem with General Utility Functions by Yan Zhang, Peibiao Zhao

“…Moreover, applying the dual method along with the partial differential equation method, we verify the asymptotic behavior of the optimal control strategy, which means that the optimal investment-reinsurance strategy with the general utility functions converges to that with the power utility function at any level of the initial wealth.…”
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Numerical Solutions to Optimal Portfolio Selection and Consumption Strategies under Stochastic Volatility by Lei Ge, Qiang Zhang

“…Based on the method of dynamic programming, this paper uses analysis methods governed by the nonlinear and inhomogeneous partial differential equation to study modern portfolio management problems with stochastic volatility, incomplete markets, limited investment scope, and constant relative risk aversion (CRRA). …”
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A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel by Shabir Ahmad, Aman Ullah, Ali Akgül, Manuel De la Sen

“…We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. …”
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Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising by V. B. Surya Prasath, Arindama Singh

“…We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. …”
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Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media by Piyush R. Mistry, Vikas H. Pradhan, Khyati R. Desai

“…An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.…”
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Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme by Dagnachew Mengstie Tefera, Awoke Andargie Tiruneh, Getachew Adamu Derese

“…This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. …”
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DYNAMIC CHARACTERISTICS ANALYSIS OF SPHERICAL HYBRID SLIDING BEARINGS by JI DongSheng, SHEN JingFeng, CHEN YuFei, ZHOU YiHao

“…Taking spherical hybrid sliding bearings as the research object, established the mathematical model of lubrication analysis of spherical sliding bearings, the dynamic liquid lubrication equation under laminar flow was derived by the perturbation method, the partial differential equation of disturbance pressure was solved by the finite difference method, and the liquid was calculated numerically. …”
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The Extended Trial Equation Method for Some Time Fractional Differential Equations by Yusuf Pandir, Yusuf Gurefe, Emine Misirli

“…Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. …”
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On the Korteweg-de Vries equation: an associated equation by Eugene P. Schlereth, Ervin Y. Rodin

“…The purpose of this paper is to describe a relationship between the Korteweg-de Vries (KdV) equation ut−6uux+uxxx=0and another nonlinear partial differential equation of the form zt+zxxx−3zxzxxz=H(t)z.The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. …”
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Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient by Te-Wen Tu, Sen-Yung Lee

“…By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. …”
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Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity by Adil Jhangeer, Abdallah M. Talafha, Ariana Abdul Rahimzai, Lubomír Říha

“…The transformation of the coupled partial differential equation into ordinary differential equation is achieved by utilizing a complex wave variable. …”
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An Improved C-V Model and Application to the Coal Rock Mesocrack Images by Yulong Chen, Hongwei Zhang

“…In order to accurately and comprehensively obtain information about coal rock mesocrack images, image processing technique based on partial differential equation (PDE) is introduced in order to expound on the active contour model without edges and overcome the deficiency of the C-V model. …”
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Iterative Learning Control with Forgetting Factor for Linear Distributed Parameter Systems with Uncertainty by Xisheng Dai, Senping Tian, Wenguang Luo, Yajun Guo

“…Finally, by using the forward difference scheme of partial differential equation to solve the problems, the simulation results are presented to illustrate the feasibility of the algorithm.…”
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In Situ Bioremediation of Crude Petroleum Oil Polluted Soil Using Mathematical Experimentation by Modupe Elizabeth Ojewumi, Moses Eterigho Emetere, Damilola Elizabeth Babatunde, Joshua Olusegun Okeniyi

“…The parabolic partial differential equation developed was resolved into a system of ordinary differential equations (ODEs) by orthogonal collocation method and the necessary boundary condition was used. …”
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Per‐unit transformation for the combined analysis of multi‐energy integration by Zhang Zhang, Fei Wang, Hui Fan

“…Abstract To handle numerical issues caused by dimensional differences among heterogeneous states in integrated energy systems (IES), this paper proposes a novel per‐unit transformation method and explores its applications to the partial differential equation‐governed models. Initially, a unified IES model is developed, which encompasses both fast and slow dynamics in a generalized form. …”
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Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics by Rafael A. Penchel, José R. Bergmann, Fernando J. S. Moreira

“…This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. …”
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Double-Scale Expansions for a Logarithmic Type Solution to a q-Analog of a Singular Initial Value Problem by Stéphane Malek

“…The equation under study represents a q−analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. …”
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High-Accurate Numerical Schemes for Black–Scholes Models with Sensitivity Analysis by Samir Kumar Bhowmik, Jakobin Alam Khan

“…The significance of both the linear and nonlinear Black-Scholes partial differential equation model is huge in the field of financial analysis. …”
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