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