Results 261 to 270 of about 1,362,923 (320)

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

Observer-based partial differential equation boundary control for a flexible two-link manipulator in task space

, 2012
This study addresses the problem of trajectory control of a flexible two-link manipulator on the basis of the partial differential equation (PDE) dynamic model.
Linjun Zhang, Jinkun Liu
semanticscholar   +1 more source

Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time

IEEE Transactions on Image Processing, 2003
In this paper, we introduce a new method for image smoothing based on a fourth-order PDE model. The method is tested on a broad range of real medical magnetic resonance images, both in space and time, as well as on nonmedical synthesized test images. Our
O. M. Lysaker, A. Lundervold, Xuecheng Tai   +2 more
semanticscholar   +1 more source

Differential Equations: Partial

2000
We have been studying nonlinear oscillatory processes, starting with the simplest autonomous case, and later incorporating forcing. The modelling was in terms of ordinary differential equations (ODE), and the most important tool used was the phase diagram.
openaire   +2 more sources

Partial Differential Equations

1988
In this chapter, procedures will be developed for classifying partial differential equations as elliptic, parabolic or hyperbolic. The different types of partial differential equations will be examined from both a mathematical and a physical viewpoint to indicate their key features and the flow categories for which they occur.
openaire   +2 more sources

Application of the Exp‐function method for solving a partial differential equation arising in biology and population genetics

, 2011
Purpose – The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.Design/methodology/approach – This technique is straightforward and simple to use and is a ...
M. Dehghan, J. M. Heris, A. Saadatmandi
semanticscholar   +1 more source

Partial Differential Equations

1978
As an example to show how the Laplace transform may be applied to the solution of partial differential equations, we consider the diffusion of heat in an isotropic solid body.
openaire   +2 more sources

Partial Differential Equations

2012
In this chapter we study some classes of partial differential equations, including the heat equation, the Laplace equation, and the wave equation. In particular, based on the study of Fourier series, we find solutions for several equations and several types of boundary conditions. We mainly use the method of separation of variables. In contrast to what
Luis Barreira, Claudia Valls
openaire   +4 more sources

Partial Differential Equation Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs

, 2010
We derive a partial differential equation (PDE) representation for the value of financial derivatives with bilateral counterparty risk and funding costs.
Christoph Burgard, Mats Kjaer
semanticscholar   +1 more source

Partial Differential Equations [PDF]

, 2001
Many physical problems involve quantities that depend on more than one variable. The temperature within a “large”1 solid body of conducting material varies with both time and location within the material. When such problems are modeled, what results is a differential equation involving partial derivatives, or a partial differential equation..
openaire   +1 more source