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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

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 ...
Weinan E, Jiequn Han, Arnulf Jentzen
semanticscholar +1 more source

Partial Differential Equations

Principles of Applied Mathematics, 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
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Fractal Solitons, Arbitrary Function Solutions, Exact Periodic Wave and Breathers for a Nonlinear Partial Differential Equation by Using Bilinear Neural Network Method

Journal of Systems Science and Complexity, 2020
Runfa Zhang, S. Bilige, T. Chaolu
semanticscholar +1 more source

Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types

Nonlinear dynamics, 2021
Xing Lü, Sijia Chen
semanticscholar +1 more source

A general memristor-based partial differential equation solver