Practical Runge-Kutta processes
SIAM Journal on Scientific and Statistical Computing
VODE: a variable-coefficient ODE solver
SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A note on stability of the Douglas splitting method
Mathematics of Computation
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
SIAM Journal on Scientific Computing
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
Journal of Computational Physics
Approximate factorization for time-dependent partial differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Operator splitting and approximate factorization for taxis-diffusion-reaction models
Applied Numerical Mathematics
Accuracy and stability of splitting with stabilizing corrections
Applied Numerical Mathematics
RKC time-stepping for advection-diffusion-reaction problems
Journal of Computational Physics
An iterated Radau method for time-dependent PDEs
Journal of Computational and Applied Mathematics
Linearly implicit Runge--Kutta methods and approximate matrix factorization
Applied Numerical Mathematics
A variable time-step-size code for advection-diffusion-reaction PDEs
Applied Numerical Mathematics
A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
The numerical integration of PDEs of Advection-Diffusion-Reaction type in several spatial variables in the MoL framework is considered. The spatial discretization is based on Finite Differences and the time integration is carried out by using splitting techniques applied to Rosenbrock-type methods. The focus here is to provide a way of making some refinements to the usual Approximate Matrix Factorization (AMF) when it is applied to some well-known Rosenbrock-type methods. The proposed AMF-refinements provide new methods in a natural way and some of these methods belong to the class of the W-methods. Interesting stability properties of the resulting methods are proved and a few numerical experiments on some important non-linear PDE problems with applications in Physics are carried out.