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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