Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order by Asma Ali Elbeleze, Adem Kılıçman, Bachok M. Taib

“…We are concerned here with singular partial differential equations of fractional order (FSPDEs). The variational iteration method (VIM) is applied to obtain approximate solutions of this type of equations. …”
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Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay by Brajesh Kumar Singh, Pramod Kumar

“…This paper deals with an alternative approximate analytic solution to time fractional partial differential equations (TFPDEs) with proportional delay, obtained by using fractional variational iteration method, where the fractional derivative is taken in Caputo sense. …”
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Research on boundary control of vehicle-mounted flexible manipulator based on partial differential equations. by Yuzhi Tang

“…We present a novel mathematical model, derived using Hamilton's principle, which simplifies the analysis of the arm's dynamic behaviors by employing partial differential equations (PDEs). This model allows us to understand how these arms behave over time and space, classifying them as distributed parameter systems. …”
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Solutions of Nonlinear Integro-Partial Differential Equations by the Method of G′/G,1/G by Daba Meshesha Gusu, Chala Bulo

“…In this article, a special expansion method is implemented in solving nonlinear integro-partial differential equations of 2+1-dimensional using a special expansion method of G′/G,1/G. …”
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Urban Planning Image Feature Enhancement and Simulation Based on Partial Differential Equation Method by Duo Li

“…Based on the introduction of the basic ideas and related technologies of partial differential equations, as well as the method of path planning, the application of partial differential equations in solving urban path planning is studied. …”
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A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations by Fenglian Liu, Muhammad Nadeem, Ibrahim Mahariq, Suliman Dawood

“…In this study, we propose a new iterative scheme (NIS) to investigate the approximate solution of the fourth-order parabolic partial differential equations (PDEs) that arises in transverse vibration problems. …”
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Conservation Laws for Some Systems of Nonlinear Partial Differential Equations via Multiplier Approach by Rehana Naz

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Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical Imaging by Kiwoon Kwon

“…Unique determination issues about inverse problems for elliptic partial differential equations in divergence form are summarized and discussed. …”
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Galerkin Spectral Method of Stochastic Partial Differential Equations Driven by Multivariate Poisson Measure by Hongling Xie

“…A considerable body of prior research has been dedicated to devising efficient and high-order numerical methods for solving stochastic partial differential equations (SPDEs) driven by discrete or continuous random variables. …”
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On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method by Muhammad Sinan, Kamal Shah, Zareen A. Khan, Qasem Al-Mdallal, Fathalla Rihan

“…In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. …”
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Research on Image Recognition of Building Wall Design Defects Based on Partial Differential Equation by Xiwen Yu, Kai Wang, Shaoxuan Wang

“…Then, the improved partial differential equation is used to recognize the image as a whole. …”
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Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition by Allaberen Ashyralyev, Fadime Dal

“…The numerical and analytic solutions of the mixed problem for multidimensional fractional hyperbolic partial differential equations with the Neumann condition are presented. …”
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The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface by B. Sheehan, D. Estep, S. Tavener, J. Cary, S. Kruger, A. Hakim, A. Pletzer, J. Carlsson, S. Vadlamani

“…We investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. …”
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Research on boundary control of vehicle-mounted flexible manipulator based on partial differential equations by Yuzhi Tang

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An experimental comparison of two preconditioned iterative methods to solve the elliptic partial differential equations by Seyyed Ahmad Edalatpanah

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Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions by Fukang Yin, Junqiang Song, Yongwen Wu, Lilun Zhang

“…A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs). …”
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An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions by A. H. Bhrawy, M. A. Alghamdi, Eman S. Alaidarous

“…One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs) as well as PDEs with variable coefficients. …”
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Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations by Jagdev Singh, Devendra Kumar, Adem Kılıçman

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Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations by Jafar Biazar, Mohammad Hosami

“…Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. …”
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Some maximum principles for solutions of a class of partial differential equations in Ω⊂ℝn by Mohammad Mujalli Al-Mahameed

“…We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1) Δ2u+αf(u)=0, α∈ℝ+ and (2) ΔΔu+α(Δu)k+gu=0, α≤0 in some region Ω⊂ℝn.…”
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