The impact of finite precision arithmetic and sensitivity on the numerical solution of partial differential equations

DOI10.1016/S0895-7177(02)00078-XzbMath1060.65116MaRDI QIDQ1876777

James M. Hill, John A. Burns, David S. Gilliam, Victor Shubov, Edward J. Allen

Publication date: 20 August 2004

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

zbMATH Keywords

sensitivityalgorithmstabilityBurgers equationsteady state problemsnonuniquenessfinite precision arithmeticmarching schemesfalse numerical solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (4)

Finite element approximation to global stabilization of the Burgers' equation by Neumann boundary feedback control law ⋮ Boundary control of a coupled Burgers' PDE‐ODE system ⋮ Методика связанного моделирования одномерных и трехмерных задач вычислительной гидродинамики ⋮ A statistical version of prophet inequalities

Cites Work

• Convergence to steady state of solutions of Burgers' equation
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• Multiple steady states for characteristic initial value problems
• On the global dynamics of a controlled viscous Burgers' equation
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• Asymptotic-Numerical Study of Supersensitivity for Generalized Burgers' Equations
• On the exponentially slow motion of a viscous shock
• The partial differential equation u_t + uu_x = μ_xx
• Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations
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