A family of finite difference methods is developed for the numerical solution of the simple wave equation. Local truncation errors are cal- culated for each member of the family and each is analyzed for stability. The concepts of A0 -stability and L0 -stability, well-used in the literature on other types of partial differential equation, are discussed in relation to second order hyperbolic equations. The numerical methods are extended to cover two-dimensional wave equations and the methods developed in the paper are tested on three problems from the literature.
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