Approximate Solutions and Error Bounds for Quasi-Linear Hyperbolic Initial Boundary Value Problems

For a given quasilinear hyperbolic initial boundary value problem whose nonlinear part is convex, constrained minimization problems (CMP) are formulated, making use of a minimum principle of the hyperbolic equation. Approximate solutions and two error bounds of the given initial boundary value probl...

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Veröffentlicht in:SIAM journal on numerical analysis Jg. 12; H. 1; S. 37 - 45
1. Verfasser: Cheung, To-Yat
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 01.03.1975
Schlagworte:
Approximation
Boundary value problems
Error bounds
Error rates
Linear programming
Mathematical tables
Minimum principle
ISSN:0036-1429, 1095-7170
Online-Zugang:Volltext
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Zusammenfassung:For a given quasilinear hyperbolic initial boundary value problem whose nonlinear part is convex, constrained minimization problems (CMP) are formulated, making use of a minimum principle of the hyperbolic equation. Approximate solutions and two error bounds of the given initial boundary value problem can be obtained by solving these CMP's, using linear programming methods and numerical approximation techniques. The CMP's are iterative processes. Each iterative cycle consists of two steps. Starting with some guessed approximation, Step 1 improves the solution by solving a linear program whose constraints are quasi-linearizations of the given problem and whose objective function is a linear function of the defects of the constraints. Step 2 is also a linear program, whose constraints are an auxiliary system of the given problem. Error bounds are formed from the solutions of Step 1 and Step 2. The approximate solutions are obtained by minimizing the error bounds in a certain sense. Numerical results are included.
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ISSN:0036-1429
1095-7170
DOI:10.1137/0712003