Results 1 to 10 of about 86,380,618 (176)
Multidimensional transonic shock waves and free boundary problems [PDF]
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
doaj +4 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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 +2 more
doaj +1 more source
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 +3 more
doaj +1 more source
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 +4 more
doaj +1 more source
Mesh-Free RBF-FD Method with Polyharmonic Splines and Polynomials for High-Dimensional PDEs and Financial Option Pricing [PDF]
Control and Optimization in Applied MathematicsThis study employs the radial basis function-generated finite difference (RBF-FD) method to address high-dimensional elliptic differential equations under Dirichlet boundary conditions.
Narges Hosseinzadeh +2 more
doaj +1 more source
Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications [PDF]
Geoscientific Model DevelopmentThe 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
doaj +1 more source
On numerical simulation of liquid polymer moulding
Mathematical Modelling and Analysis, 2003 In this paper we consider numerical algorithms for solving the system of nonlinear PDEs, arising in modeling of liquid polymer injection. We investigate the particular case when a porous preform is located within the mould, so that the liquid polymer is ...
R. Čiegis, O. Iliev
doaj +1 more source