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A family of methods for the wave equation in one‐ and two‐space dimensions
Author(s) -
Twizell E. H.,
Tirmizi S. I. A.
Publication year - 1985
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690010203
Subject(s) - mathematics , hyperbolic partial differential equation , stability (learning theory) , mathematical analysis , wave equation , partial differential equation , truncation (statistics) , ftcs scheme , space (punctuation) , differential equation , ordinary differential equation , differential algebraic equation , linguistics , statistics , philosophy , machine learning , computer science
A family of finite‐difference methods is developed for the numerical solution of the simple wave equation. Local truncation errors are calculated for each member of the family and each is analyzed for stability. The concepts of A 0 stability and L 0 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 arc extended to cover two‐dimensional wave equations and the methods developed in this article are tested on three problems from the literature.