Runge-kutta solutions of a hyperbolic conservation law with source term

SIAM Journal on Scientific Computing

Volumn 22, Issue 1, 2000, Pages 20-38

  Aves, M A ^a   Griffiths, D F ^a   Higham, D J ^a  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

Adaptivity; Finite difference; Nonnormality; Spurious solution; Steady state

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FINITE DIFFERENCE METHOD; INITIAL VALUE PROBLEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; POLYNOMIALS; THEOREM PROVING;

ADAPTIVITY; NONNORMALITY; STEADY STATE;

RUNGE KUTTA METHODS;

EID: 0034455663     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S106482759833601X     Document Type: Article

References (24)

1. Does error control suppress spuriosity?
2. On the solution of convection-diffusion boundary value problems using equidistributed grids
3. Robust difference approximation of stiff inviscid detonation waves
4. Stable periodic bifurcations of an explicit discretization of a nonlinear partial differential equation in reaction diffusion
5. Numerical wave propagation in an advection equation with a nonlinear source term
6. On spurious asymptotic numerical solutions of explicit Runge-Kutta methods
7. Equilibria of Runge-Kutta methods
8. Regular Runge-Kutta pairs
9. Non-normality effects in a discretised, nonlinear, reaction-convection-diffusion equations
10. Spurious solutions of numerical methods for initial value problems
11. A positive finite-difference advection scheme
12. Stability and dynamics of numerical methods for nonlinear ordinary differential equations
13. A unified approach to spurious solutions introduced by time discretisation. Part I: Basic theory
14. A study of numerical methods for hyperbolic conservation laws with stiff source terms
15. Period three implies chaos
16. Stability of the method of lines
17. Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
18. Bifurcations of hyperbolic fixed points for explicit Runge-Kutta methods
19. On the dynamics of some grid-adaption schemes
20. Dynamical systems approach study of spurious steady state numerical solutions of nonlinear differential equations. 1. The ODE connection and its implications for algorithm developments in computational fluid dynamics