Results 11 to 20 of about 1,407,788 (320)

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Journal of Computational Physics, 2019
We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations.
M. Raissi, P. Perdikaris, G. Karniadakis
semanticscholar   +3 more sources

On the Fundamental Analyses of Solutions to Nonlinear Integro-Differential Equations of the Second Order

Mathematics, 2022
In this article, a scalar nonlinear integro-differential equation of second order and a non-linear system of integro-differential equations with infinite delays are considered.
Cemil Tunç, Osman Tunç
doaj   +1 more source

On Removable Singularities of Solutions of Higher-Order Differential Inequalities

Advanced Nonlinear Studies, 2020
We obtain sufficient conditions for solutions of the mth-order differential ...
Kon’kov A. A., Shishkov A. E.
doaj   +1 more source

Meromorphic solutions of nonlinear ordinary differential equations [PDF]

, 2010
Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of many methods for
Aslan, Assas, Bateman, Benney, Berloff, Billingham, Burgers, Cohen, Cole, Dai, Drazin, Eremenko, Fu, Hopf, Inan, Kangalgil, Korteweg, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kuramoto, Köroglu, Li, Li, Nikolai A. Kudryashov, Parkes, Parkes, Salas, Sarma, Shang, Shkadov, Sivashinsky, Topper, Wang, Wazzan, Wen, Whitham, Yu, Zhang, Zhang, Zheng, Zhu   +52 more
core   +1 more source

Quantum computing for nonlinear differential equations and turbulence [PDF]

Nature Reviews Physics
Many problems in classical physics and engineering, such as turbulence, are governed by nonlinear differential equations, which typically require high-performance computing to be solved.
Felix Tennie, Sylvain Laizet, S. Lloyd, Luca Magri   +3 more
semanticscholar   +1 more source

A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces [PDF]

Nonlinear Analysis, 2018
The Musielak–Orlicz setting unifies variable exponent, Orlicz, weighted Sobolev, and double-phase spaces. They inherit technical difficulties resulting from general growth and inhomogeneity.
Iwona Chlebicka
semanticscholar   +1 more source

A method for constructing a complete bifurcation picture of a boundary value problem for nonlinear partial differential equations: application of the Kolmogorov-Arnold theorem [PDF]

Известия высших учебных заведений: Прикладная нелинейная динамика
The purpose of this study is to develop a numerical method for bifurcation analysis of nonlinear partial differential equations, based on the reduction of partial differential equations to ordinary ones, using the Kolmogorov-Arnold theorem.
Gromov, Vasily Alexandrovich, Tomashchuk, Korney Kirillovich, Beschastnov, Yury Nikolaevich, Sidorenko, Artem Aleksandrovich, Kakurin, Vasily Vladimirovich   +4 more
doaj   +1 more source

Weak Continuity and Compactness for Nonlinear Partial Differential Equations [PDF]

, 2015
We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role.
Chen, Gui-Qiang G.
core   +1 more source

The amazing fractional Maclaurin series for solving different types of fractional mathematical problems that arise in physics and engineering

Partial Differential Equations in Applied Mathematics, 2023
Many applications and natural phenomena in the fields of physics and engineering are described by ordinary and partial differential equations. Therefore, obtaining solutions to these equations helps to analyze and understand the dynamics of these systems,
Marwan Alquran
doaj   +1 more source

On Linear Differential Equations Involving a Para-Grassmann Variable [PDF]

, 2009
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly.
Mansour, Toufik, Schork, Matthias
core   +5 more sources