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- W201622078 abstract "This chapter discusses the construction of stable difference methods for the initial-boundary value problem for hyperbolic partial differential equations. There is a general stability theory of Gustafsson, Kreiss, and Sundstrom for these approximations, which provides necessary and sufficient conditions for stability. This theory is a posteriori in nature. Given a difference method, this theory can be used to determine whether the method is stable, but there is little insight provided to guide in the construction of a stable method. The chapter presents certain conditions that are sufficient for stability, are easily verified, and are applicable to a large class of approximations. These conditions can be used in the construction of stable methods for the initial-boundary value problem. The sufficient conditions involve properties of methods for related Cauchy problems: consistency, stability for the Cauchy problem, and dissipativity. These conditions are usually known or easily verified by standard techniques." @default.
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- W201622078 date "1979-01-01" @default.
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- W201622078 title "Constructing Stable Difference Methods for Hyperbolic Equations" @default.
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- W201622078 doi "https://doi.org/10.1016/b978-0-12-546050-7.50013-7" @default.
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