Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I. The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Journal of Computational Physics

Volumn 97, Issue 2, 1991, Pages 249-310

  Yee, H C ^a   Sweby, P K ^b   Griffiths, D F ^c  

^a NASA AMES RESEARCH CENTER   (United States)

^b UNIVERSITY OF READING   (United Kingdom)

^c UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042829361     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/0021-9991(91)90001-2     Document Type: Article

References (123)

1. NASA Computational Fluid Dynamics Conference
2. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part II. System of 2 × 2 ODEs
3. Stability of Spurious Steady-State Solutions of Runge-Kutta and Related Methods for PDEs
4. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part IV. Stability vs Methods of Discretizing Nonlinear Source Terms
5. Finite Amplitude Instabilities of Partial Difference Equations
6. Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations
7. Uniqueness and the Cell Reynolds Number
8. Multiple Solutions and Bifurcation of Finite Difference Approximations to Some Steady Problems of Fluid Dynamics
9. Proceedings, Nonlinear Hyperbolic Equations
10. Period Three Implies Chaos
11. The problem of deducing the climate from the governing equations
12. Behavior of Dynamical Systems Governed by a Simple Nonlinear Difference Equation
13. A Horror Story about Integration Methods
14. Turbulence in Multistep Methods for Initial Value Problems
15. A numerical study of chaos in a reaction-diffusion equation
16. Stable Periodic Solutions in Nonlinear Difference Equations
17. Multiple Solutions of the Transonic Potential Flow Equation
18. Discrete Dynamical Systems in Dimensions One and Two
19. Implicit Numerical Methods for the Compressible Navier-Stokes and Euler Equations
20. On the Construction and Comparison of Difference Schemes
21. The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations
22. The approach of solutions of nonlinear diffusion equations to travelling front solutions
23. Theoretical and Numerical Structure for Reacting Shock Waves
24. An investigation of the Dynamical Behavior of a Nonlinear Reaction-Advection Equation under Discretization
25. Systems of conservation laws
26. Hyperbolic Conservation Laws and Numerical Methods
27. A two-dimensional mapping with a strange attractor
28. AUTO: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations
29. Estimation and Reduction of Numerical Error
30. Difference schemes for hyperbolic equations with high order of accuracy
31. Numerical Simulation of Chaotic Flows: Measures of Chaos