Results 11 to 20 of about 33,202 (148)

Multidimensional transonic shock waves and free boundary problems

Bulletin of Mathematical Sciences, 2022
We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics.
Gui-Qiang G. Chen, Mikhail Feldman
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PINNs algorithm and its application in geotechnical engineering

Yantu gongcheng xuebao, 2021
The physical information neural networks (PINNs) algorithm, a new mesh-free algorithm, uses the automatic differential method to embed the partial differential equation directly into the neural networks so as to realize the intelligent solution of the ...
LAN Peng 1, LI Hai-chao 1, YE Xin-yu 1, ZHANG Sheng 1, SHENG Dai-chao 1, 2
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Finite line method for solving high-order partial differential equations in science and engineering

Partial Differential Equations in Applied Mathematics, 2023
In this paper, a completely new numerical method, named Finite Line Method (FLM), is proposed for solving general linear and non-linear high-order partial differential equations (PDEs) in science as well as engineering problems in heat conduction and ...
Xiao-Wei Gao, Yu-Mo Zhu, Tao Pan
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Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy

Mathematics, 2021
We study nonlinear pantograph-type reaction–diffusion PDEs, which, in addition to the unknown u=u(x,t), also contain the same functions with dilated or contracted arguments of the form w=u(px,t), w=u(x,qt), and w=u(px,qt), where p and q are the free ...
Andrei D. Polyanin, Vsevolod G. Sorokin
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Extending Density Phase-Field Simulations to Dynamic Regimes

Metals, 2023
Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry ...
David Jacobson, Reza Darvishi Kamachali, Gregory Bruce Thompson   +2 more
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High precision compact numerical approximation in exponential form for the system of 2D quasilinear elliptic BVPs on a discrete irrational region

MethodsX, 2022
This article presents a new approximation of order four in exponential form for two-dimensional (2D) quasilinear partial differential equation (PDE) of elliptic form with solution domain being irrational.
R.K. Mohanty, Nikita Setia, Gunjan Khurana, Geetan Manchanda   +3 more
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Geometry aware physics informed neural network surrogate for solving Navier–Stokes equation (GAPINN)

Advanced Modeling and Simulation in Engineering Sciences, 2022
Many real world problems involve fluid flow phenomena, typically be described by the Navier–Stokes equations. The Navier–Stokes equations are partial differential equations (PDEs) with highly nonlinear properties. Currently mostly used methods solve this
Jan Oldenburg, Finja Borowski, Alper Öner, Klaus-Peter Schmitz, Michael Stiehm   +4 more
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Solving high-order partial differential equations with indirect radial basis function networks [PDF]

, 2005
This paper reports a new numerical method based on radial basis function networks (RBFNs) for solving high-order partial differential equations (PDEs).
Mai-Duy, N., Tanner, R. I.
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Lie symmetries of nonlinear boundary value problems [PDF]

, 2012
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs.
Alexiades, Andreev, Barry, Benjamin, Bluman, Bluman, Bluman, Briozzo, Britton, Broadbridge, Carslaw, Cherniha, Cherniha, Cherniha, Cherniha, Cherniha, Cherniha, Cherniha, Crank, Fushchych, Galaktionov, Ibragimov, King, Kudryashov, Lorenzo-Trueba, Ma, Ma, Malfliet, Olver, Olver, Ovsiannikov, Polyanin, Pukhnachov, Pukhnachov, Ready, Rogers, Roman Cherniha, Rubinstein, Sergii Kovalenko, Sidorov, Stefan, Voller, Wang, Wazwaz   +43 more
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Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications [PDF]

Geoscientific Model Development
The accelerated pseudo-transient (APT) method is a matrix-free approach used to solve partial differential equations (PDEs), characterized by its reliance on local operations, which makes it highly suitable for parallelization.
Y. Alkhimenkov, Y. Y. Podladchikov
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