Exact Finite-Difference Schemes

✍ Scribed by Sergey Lemeshevsky (editor); Piotr Matus (editor); Dmitriy Poliakov (editor)

Publisher: De Gruyter
Year: 2016
Tongue: English
Leaves: 246
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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

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