The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Automatic selection of the initial step size for an ODE solver
Journal of Computational and Applied Mathematics
Efficient numerical path following beyond critical points
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Diagonally-implicit multi-stage integration methods
Applied Numerical Mathematics
Applied Numerical Mathematics
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
A nonlinear optimization approach to the construction of general linear methods of high order
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
Exploiting structure in the construction of DIMSIMs
Journal of Computational and Applied Mathematics
Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4]
ACM Transactions on Mathematical Software (TOMS)
A locally parameterized continuation process
ACM Transactions on Mathematical Software (TOMS)
Algorithm 596: a program for a locally parameterized
ACM Transactions on Mathematical Software (TOMS)
Implementation of DIMSIMs for stiff differential systems
Applied Numerical Mathematics
Digital filters in adaptive time-stepping
ACM Transactions on Mathematical Software (TOMS)
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Error propagation of general linear methods for ordinary differential equations
Journal of Complexity
Hi-index | 0.00 |
It it the purpose of this paper to review the results on the construction and implementation of diagonally implicit multistage integration methods for ordinary differential equations. The systematic approach to the construction of these methods with Runge---Kutta stability is described. The estimation of local discretization error for both explicit and implicit methods is discussed. The other implementations issues such as the construction of continuous extensions, stepsize and order changing strategy, and solving the systems of nonlinear equations which arise in implicit schemes are also addressed. The performance of experimental codes based on these methods is briefly discussed and compared with codes from Matlab ordinary differential equation (ODE) suite. The recent work on general linear methods with inherent Runge---Kutta stability is also briefly discussed