Abstract
Obviously, the purpose of this book is not to provide a general theory of stability for numerical approximations of ordinary differential equations. This has already been done by specialists (see for example [58] or [62]). What we are going to do here is give an intuitive approach to the notion of stability of a scheme for the wave equations. This approach is actually based on plane wave solutions which can be regarded as elementary solutions of the wave equations, as we saw in Sect. 3.1.KeywordsStability ConditionWave EquationDispersion RelationNumerical IllustrationDiscrete OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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