Results 251 to 260 of about 1,551,677 (306)

Fractional Order Pseudoparabolic Partial Differential Equation: Ulam–Hyers Stability

Bulletin of the Brazilian Mathematical Society, New Series, 2018
Using Gronwall inequality we will investigate the Ulam-Hyers and generalized Ulam–Hyers–Rassias stabilities for the solution of a fractional order pseudoparabolic partial differential equation.
J. Vanterler, DA C. Sousa, E. C. Oliveira   +2 more
semanticscholar   +1 more source

Partial Differential Equations

2010
A. Laptev
openaire   +3 more sources

Stochastic partial differential equations

2014
Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2.
Peter K. Friz, Martin Hairer
openaire   +1 more source

Complex Partial Differential Equations

Journal of Mathematical Sciences
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aksoy, Ü., Begehr, H., Çelebi, A., Shupeyeva, B.   +3 more
openaire   +1 more source

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

Communications in Mathematics and Statistics, 2017
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of ...
W. E, Jiequn Han, Arnulf Jentzen
semanticscholar   +1 more source

Partial Differential Equations

1999
[no abstract available]
  +4 more sources

Partial Differential Equations and Difference Equations

Proceedings of the American Mathematical Society, 1965
(1. 1) Pi(alax)y = ? (1 _ i _ m) where x = (x1, * , xn), a/ax = (a/ax1, *, O/0xn). The Pi's are assumed to be homogeneous polynomials with real coefficients. The term solution is used to include the generalized solutions. A generalized solution is any function continuous on R which is a uniform limit on compact subsets of CX solutions (see [2, p. 65]).
openaire   +2 more sources

Partial differential equations

2020
This chapter discusses partial differential equations (PDEs). It begins by presenting elementary cases of PDEs, which highlights that PDEs give rise to 'functions of integration', in contrast to ordinary differential equations (ODEs), which have 'constants of integration'.
D.S. Sivia, J.L. Rhodes, S.G. Rawlings
openaire   +1 more source

Partial Differential Equations II

2002
Partial differential equations of the form $$k{\partial \over {\partial t}}u(r,t) = \nabla ^2 u(r,t)$$ (diffusion equation) and $${{\partial ^2 } \over {\partial t^2 }}u(r,t) = c^2 \nabla ^2 u(r,t)$$ (wave equation) are amenable to the use of the Laplace transform.1 Indeed, on taking the Laplace transform of the former, we get ...
openaire   +1 more source

Partial Differential Equations

Numerical Python, 2018
In the following exercises we assume U is open, bounded set, with smooth boundary, and T > 0. Exercise 16 still has some gap to be overcame. The difficult exercise 9 is solved by mimicking a proof in a paper of Brezis-Evans on 2016/07/31. 1.
Boris Zaltzman
semanticscholar   +1 more source