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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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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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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Double Stratified Mixed Convective Flow of Couple Stress Nanofluid past Inclined Stretching Cylinder Using Cattaneo-Christov Heat and Mass Flux Model by Wubshet Ibrahim, Gosa Gadisa

“…The governing partial differential equation of the boundary layer flow region is reduced to its corresponding ordinary differential equation using a similarity transformation technique. …”
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Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method by Alemayehu Tamirie Deresse

“…According to the findings, the proposed method is being used to solve additional forms of nonlinear fractional partial differential equation systems. Moreover, the conformable fractional triple Laplace transform iterative method has a small computational size as compared to other methods.…”
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Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation by Shu-Li Mei, De-Hai Zhu

“…Then, combining with the finite difference technology, a new numerical method for the time fractional partial differential equation is constructed. A simple Fokker-Planck equation is taken as an example to illustrate the effectiveness by comparing with the Grunwald-Letnikov central difference approximation (GL-CDA).…”
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Thermal Diffusivity Identification of Distributed Parameter Systems to Sea Ice by Liqiong Shi, Zhijun Li, Enmin Feng, Yila Bai, Yu Yang

“…A method of optimal control is presented as a numerical tool for solving the sea ice heat transfer problem governed by a parabolic partial differential equation. Taken the deviation between the calculated ice temperature and the measurements as the performance criterion, an optimal control model of distributed parameter systems with specific constraints of thermal properties of sea ice was proposed to determine the thermal diffusivity of sea ice. …”
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Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control by Kun Yuan, Abdulaziz Alofi, Jinde Cao, Abdullah Al-Mazrooei, Ahmed Elaiw

“…By combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. …”
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HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation by Shu-Li Mei, De-Hai Zhu

“…The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. …”
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Global dynamics of a vector-host epidemic model with age of infection by Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva

“…In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. …”
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Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar by Bole Ma, Yongsheng Ren

“…The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. …”
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Richards equation for the assessment of landslide hazards by Ramesh Chandra Timsina

“…However, as a highly nonlinear parabolic partial differential equation (PDE), it has limited analytic solutions, which often lack precision in practical scenarios. …”
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Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation by Yan-Lei Zhang, Hui-Rong Feng, Li-Qun Chen

“…The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. …”
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Simulation and Domain Identification of Sea Ice Thermodynamic System by Bing Tan, Peng Lu, Zhijun Li, Enmin Feng, Juan Wang

“…Based on the measured data and characteristics of sea ice temperature distribution in space and time, this study is intended to consider a parabolic partial differential equation of the thermodynamic field of sea ice (coupled by snow, ice, and sea water layers) with a time-dependent domain and its parameter identification problem. …”
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Optimal investment game for two regulated players with regime switching by Lin Xu, Linlin Wang, Hao Wang, Liming Zhang

“…In the first case, the associated Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation was an elliptic partial differential equation (PDE). By solving an auxiliary problem, we demonstrated the existence and regularity of the value function. …”
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Preface by Azmy S. Ackleh, Linda J. S. Allen, Graciela Canziani, Shandelle M. Henson, Jia Li, Zhien Ma

“…In Athens, he became interested inecotoxicology and partial differential equation models ofphysiologically structured populations. …”
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Vibration of a Cylindrical Tunnel under a Centric Point-Source Explosion by Yuetang Zhao, Cheng Chu, Anastasios Vafeidis, Jie Li

“…The governing equation of the motion is a fourth-order partial differential equation, for which a numerical method combining finite difference with the implicit Newmark-β method was adopted. …”
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Urban Lead: Modeling Its Distribution and Effects on Children by Zhixiong Chen, Yi Ding, Andrew Getz, Bernard Lipat

“…The model is constructed using the diffusion-advection partial differential equation in three spatial dimensions and one temporal dimension with an initial condition and boundary conditions. …”
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