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 notationPreliminary resultsHyperbolic equationsParabolic equationsUse of exact
difference schemes to construct NSFD discretizations of differential equationsExact and
truncated difference schemes for boundary-value problemExact difference schemes for stochastic
differential equationsNumerical blow-up timeBibliography
