Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Iterative schemes for three-stage implicit Runge-Kutta methods
Applied Numerical Mathematics
ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs
Applied Numerical Mathematics - Special issue on time integration
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
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
A new approximate matrix factorization for implicit time integration in air pollution modeling
Journal of Computational and Applied Mathematics
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
Superconvergent explicit two-step peer methods
Journal of Computational and Applied Mathematics
High-order linearly implicit two-step peer -- finite element methods for time-dependent PDEs
Applied Numerical Mathematics
An iterated Radau method for time-dependent PDEs
Journal of Computational and Applied Mathematics
Rosenbrock-type 'Peer' two-step methods
Applied Numerical Mathematics
Linearly-implicit two-step methods and their implementation in Nordsieck form
Applied Numerical Mathematics
A variable time-step-size code for advection-diffusion-reaction PDEs
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
For the efficient solution of large stiff systems resulting from semidiscretization of multi-dimensional partial differential equations two methods using approximate matrix factorizations (AMF) are discussed. In extensive numerical tests of Reaction Diffusion type implemented in Matlab they are compared with integration methods using Krylov techniques for solving the linear systems or to approximate exponential matrices times a vector. The results show that for low and medium accuracy requirements AMF methods are superior. For stringent tolerances peer methods with Krylov are more efficient.