Overview
Read this article from a comprehensive knowledge base, updated and supplemented with articles reviewed by scientific committees.
Read the articleAUTHOR
-
Guy CHAVENT: Professor of Mathematics at Paris-Dauphine University - Scientific Director at the French National Institute for Research in Computer Science and Control (INRIA-Rocquencourt)
INTRODUCTION
In this article, we focus on the discretization of partial differential equations, in which the unknown is a function u (temperature, for example) depending on several space variables x
1
... x
n
(abbreviated to x) and time t. We'll call Ω the domain of space and [0, T] the time interval where we're trying to find out the temperature. Thus, the evolution of the temperature (u (x, t )) in an infinite bar
and homogeneous from a known initial temperature (u
0
(x )) is given by :
where c is the heat capacity and a is the thermal conductivity of the bar. The finite-difference method was historically the first known method for calculating an approximate solution of
(1)
on a computer. The idea was to replace the search for the function u (x, t ) by that of a vector (
The Ultimate Scientific and Technical Reference
This article is included in
Mathematics
This offer includes:
Knowledge Base
Updated and enriched with articles validated by our scientific committees
Services
A set of exclusive tools to complement the resources
Practical Path
Operational and didactic, to guarantee the acquisition of transversal skills
Doc & Quiz
Interactive articles with quizzes, for constructive reading
Approximation of partial differential equations
What is a finite-difference diagram?
References
The Ultimate Scientific and Technical Reference
