Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
|Original language||English (US)|
|Title of host publication||Asymptotic Analysis and the Numerical Solution of Partial Differential Equations|
|Number of pages||22|
|State||Published - Jan 1 1991|
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