Stability theory of difference approximations for multidimensional initial-boundary value problems
نویسندگان
چکیده
منابع مشابه
Stability Theory of Difference Approximations for Multidimensional Initial-Boundary Value Problems
A stability theory is developed for dissipative difference approximations to multidimensional initial-boundary value problems. The original differential problem should be strictly hyperbolic and the difference problem consistent with the differential one. An algebra of pseudo-difference operators is built and later used to prove the stability of the difference approximation with variable coeffi...
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New convenient stability criteria are provided in this paper for a large class of finite-difference approximations to initial-boundary value problems associated with the hyperbolic system u, = Auv + flu + f in the quarter plane x > 0, t > 0. Using the new criteria, stability is easily established for numerous combinations of well-known basic schemes and boundary conditions, thus generalizing ma...
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Easily checkable sufficient stability criteria are obtained for explicit dissipative approximations to mixed initial-boundary value problems associated with the system Uf = Aux in the quarter plane x > 0, t > 0. The criteria are given entirely in terms of the boundary conditions for the outflow unknowns. The results imply that certain well-known boundary conditions, when used in combination wit...
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The purpose of this paper is to extend the results of [4] in order to achieve more versatile, convenient stability criteria for a wide class of finite-difference approximations to initial-boundary value problems associated with the hyperbolic system u, = Aux + Bu + i in the quarter plane x > 0, / > 0. With these criteria, stability is easily established for a large number of examples, where man...
متن کاملScheme-Independent Stability Criteria for Difference Approximations of Hyperbolic Initial-Boundary Value Problems. II
Convenient stability criteria are obtained for difference approximations to initialboundary value problems associated with the hyperbolic system u, — Aux + Bu + t in the quarter plane x > 0, I > 0. The approximations consist of arbitrary basic schemes and a wide class of boundary conditions. The new criteria are given in terms of the outflow part of the boundary conditions and are independent o...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1983
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1983-0679433-2