Operator splitting and approximate factorization for taxis-diffusion-reaction models

Applied Numerical Mathematics

Volumn 42, Issue 1-3, 2002, Pages 159-176

  Gerisch, A ^a   Verwer, J G ^b  

^a MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^b CWI   (Netherlands)

Author keywords

Approximate matrix factorization; Method of lines; Operator splitting; PDEs; Positivity; Rosenbrock methods; Taxis diffusion reaction problems

Indexed keywords

APPROXIMATION THEORY; DIFFUSION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; RUNGE KUTTA METHODS;

OPERATOR SPLITTINGS;

INTEGRATION;

EID: 0036679647     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(01)00148-9     Document Type: Conference Paper

References (23)

1. Mathematical modelling of tumour invasion and metastasis
2. An implicit finite-difference algorithm for hyperbolic systems in conservation-law form
3. Conservation de la positivité lors de la discrétisation des problèmes d'évolution paraboliques
4. Pragmatic experiments with Krylov methods in the stiff ODE setting
5. A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor
6. Difference systems of second order accuracy with a divided operator for parabolic equations without mixed derivatives
7. A positive splitting method for mixed hyperbolic-parabolic systems
8. Splitting methods for the simulation of tumor angiogenesis models
9. On the positivity of low order explicit Runge-Kutta schemes applied in splitting methods
10. Solving ordinary differential equations II: Stiff and differential-algebraic problems, 2nd edn.
11. Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
12. Approximate factorization for time-dependent partial differential equations
13. A positive finite-difference advection scheme
14. Accuracy and stability of splitting with stabilizing corrections
15. Absolute monotonicity of polynomials occurring in the numerical solution of initial value problems
16. Contractivity of Runge-Kutta methods
17. Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling
18. The numerical solution of parabolic and elliptic differential equations
19. Efficient implementation of essentially non-oscillatory shock-capturing schemes
20. On the construction and comparison of difference schemes
21. Fractional step methods applied to a chemotaxis model
22. A second-order Rosenbrock method applied to photochemical dispersion problems