Exact Finite-Difference Schemes
Author： Lemeshevsky Sergey;Matus Piotr;Poliakov Dmitriy
Publisher： De Gruyter
Publication year： 2016
E-ISBN: 9783110491326
P-ISBN(Paperback): 9783110489644
Subject： O175 differential equations, integral equations
Keyword： 微分方程、积分方程,应用数学
Language： ENG
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Description
Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations.
Contents:
Basic notation
Preliminary results
Hyperbolic equations
Parabolic equations
Use of exact difference schemes to construct NSFD discretizations of differential equations
Exact and truncated difference schemes for boundary-value problem
Exact difference schemes for stochastic differential equations
Numerical blow-up time
Bibliography
Chapter