Results 1 to 10 of about 173,975,381 (346)
Isogeometric Analysis for Surface PDEs With Extended Loop Subdivision [PDF]
Journal of Computational Physics, 2019 We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the geometry exactly,
Chong Chen, Timon Rabczuk, Gang Xu
exaly +2 more sources
Numerical Bifurcation Analysis of PDEs From Lattice Boltzmann Model Simulations: a Parsimonious Machine Learning Approach [PDF]
Journal of Scientific Computing, 2022 We address a three-tier data-driven approach for the numerical solution of the inverse problem in Partial Differential Equations (PDEs) and for their numerical bifurcation analysis from spatio-temporal data produced by Lattice Boltzmann model simulations
Evangelos Galaris +4 more
semanticscholar +1 more source
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs [PDF]
Journal of Computational Physics, 2023 We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods.
Pau Batlle +4 more
semanticscholar +1 more source
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs [PDF]
Advances in Computational Mathematics, 2021 Physics-informed neural networks approximate solutions of PDEs by minimizing pointwise residuals. We derive rigorous bounds on the error, incurred by PINNs in approximating the solutions of a large class of linear parabolic PDEs, namely Kolmogorov ...
Tim De Ryck, Siddhartha Mishra
semanticscholar +1 more source
Approximation Error Analysis of Some Deep Backward Schemes for Nonlinear PDEs [PDF]
SIAM Journal on Scientific Computing, 2020 Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence properties.
Maximilien Germain +2 more
semanticscholar +1 more source
Boundary Value Problems, 2022 In this paper, we consider two internal stabilization problems for the multi-dimensional wave equation with a boundary time-delay. We prove that the first problem is well-posed in an appropriate functional space.
Kaïs Ammari +2 more
doaj +1 more source
Efficient Method for Solving System of Nonlinear PDEs
Muthanna Journal of Pure Science, 2021 This paper presents an analysis solution for systems of nonlinear partial differential equations using decomposition method. Two illustrated examples has been introduced, and the method has shown a high-precision, fast approach to solve nonlinear system
Z. H. Kareem
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Desimal, 2023 In this study, some linear PDEs and nonlinear PDEs are investigated using the homotopy perturbation method (HPM). The primary objective of this research is to employ the HPM as a tool for investigating a range of PDEs and extracting their analytical ...
Md. Mizanur Rahman +2 more
doaj +1 more source
Journal of Computational Physics, 2023 We consider the approximation of a class of dynamic partial differential equations (PDEs) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the nonlinear Klein ...
Yanxia Qian +3 more
semanticscholar +1 more source
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
doaj +1 more source