Results 331 to 340 of about 1,729,322 (384)

Partial Differential Equations

1986
The formation of ordinary linear differential equations and their solution by various methods were covered in some detail in Programmes 24, 25, 26 of the previous year’s work as presented in Engineering Mathematics (second edition) and reference to these sections before undertaking the new work of this programme could be beneficial—especially Programme
Jürgen Bliedtner, Wolfhard Hansen
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Partial Differential Equations

1994
Publisher Summary Many physical and mathematical situations are described by ordinary differential equations and others are described by partial differential equations. This chapter discusses that one way to solve some partial differential equations is the method of separation of variables.
Martha L. Abell, James P. Braselton
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Introduction to Partial Differential Equations

, 2020
These notes are based on the course Introduction to Partial Differential Equations that the author held during the Spring Semester 2019 for bachelor and master students in mathematics and physics at ETH. They are not supposed to replace the several books
G. Folland
semanticscholar   +1 more source

Optimal Control of Systems Governed by Partial Differential Equations

, 1971
Principal Notations.- I Minimization of Functions and Unilateral Boundary Value Problems.- 1. Minimization of Coercive Forms.- 1.1. Notation.- 1.2. The Case when ?: is Coercive.- 1.3. Characterization of the Minimizing Element. Variational Inequalities.-
J. Lions
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

1999
Workshop ...
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Partial Differential Equations

2019
The field of partial differential equations is arguably the workhorse of applied mathematics. While the field is steeped with a rich and fruitful history supporting volumes of research, our modest goal is to present a couple of the standard models and to show how to solve them with introductory methods.
Allen Holder, Joseph Eichholz
  +9 more sources

Deep Neural Networks Motivated by Partial Differential Equations

Journal of Mathematical Imaging and Vision, 2018
Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks.
Lars Ruthotto, E. Haber
semanticscholar   +1 more source

Partial Differential Equations

2013
There are no strict rules for the numerical treatment of partial differential equations. We concentrate here on linear partial differential equations. As an example of elliptic partial differential equations the two-dimensional Poisson equation with Dirichlet boundary conditions is investigated.
Ewald Schachinger, Benjamin A. Stickler
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Partial differential equations

2011
In this chapter and the next, the solution of differential equations of types typically encountered in the physical sciences and engineering is extended to situations involving more than one independent variable. A partial differential equation (PDE) is an equation relating an unknown function (the dependent variable) of two or more variables to its ...
K. F. Riley, M. P. Hobson
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