Numerical Methods for Initial-Boundary-Value Problems for First Order Quasilinear Hyperbolic Systems in Two Independent Variables
When discussing numerical methods for hyperbolic systems, it is usual to construct difference schemes and do theoretical analysis only for pure initial-value problems. However, most of the problems which exist in practice are initial-boundary-value problems. When applying the results from the pure initial-value problems (PIVP) to the initial-boundary-value problems (IBVP), difficulties are encountered since we usually do not know how to calculate the bounday points and how to ascertain whether an algorithm for boundary points is reasonable.
KeywordsDifference Scheme Difference Equation Boundary Point Model Problem Lipschitz Condition
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