Results 21 to 30 of about 85,369,012 (181)
An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics. [PDF]
PLoS ONE, 2014 In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is ...
Jamshad Ahmad, Syed Tauseef Mohyud-Din
doaj +1 more source
Applied Sciences, 2023 Numerical methods, such as finite element or finite difference, have been widely used in the past decades for modeling solid mechanics problems by solving partial differential equations (PDEs).
Yawen Deng +5 more
doaj +1 more source
On an inverse problem for a nonlinear third order in time partial differential equation
Results in Applied Mathematics, 2022 In this article, first we convert an inverse problem of determining the unknown timewise terms of nonlinear third order in time partial differential equation (PDE) from knowledge of two boundary measurements to the auxiliary system of integral equations.
M.J. Huntul, I. Tekin
doaj +1 more source
FDM data driven U-Net as a 2D Laplace PINN solver
Scientific Reports, 2023 Efficient solution of partial differential equations (PDEs) of physical laws is of interest for manifold applications in computer science and image analysis. However, conventional domain discretization techniques for numerical solving PDEs such as Finite
Anto Nivin Maria Antony +2 more
doaj +1 more source
Approximation of Bayesian inverse problems for PDEs [PDF]
, 2010 Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability.
Dashti, Massoumeh +6 more
core +1 more source
On some nonlinear fractional PDEs in physics
Bibechana, 2014 In this paper, we applied relatively new fractional complex transform (FCT) to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and Variational Iteration Method (VIM) is to find
Jamshad Ahmad, Syed Tauseef Mohyud-Din
doaj +3 more sources
Sparse deterministic approximation of Bayesian inverse problems [PDF]
, 2011 We present a parametric deterministic formulation of Bayesian inverse problems with an input parameter from infinite-dimensional, separable Banach spaces.
A M Stuart +5 more
core +1 more source
Machine Learning: Science and Technology, 2023 We present novel approximates of variational losses, being applicable for the training of physics-informed neural networks (PINNs). The formulations reflect classic Sobolev space theory for partial differential equations (PDEs) and their weak ...
Juan-Esteban Suarez Cardona +1 more
doaj +1 more source
The General Fractional Derivative and Related Fractional Differential Equations
Mathematics, 2020 In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
doaj +1 more source
Fully probabilistic deep models for forward and inverse problems in parametric PDEs [PDF]
, 2023 We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation leverages conventional
Arnaud Vadeboncoeur +9 more
core +4 more sources