Parallel iteration of high-order Runge-Kutta methods with stepsize control
Journal of Computational and Applied Mathematics
Diagonally-implicit multi-stage integration methods
Applied Numerical Mathematics
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
A transformation relating explicit and diagonally-implicit general linear methods
Applied Numerical Mathematics
Dimsems: diagonally implicit single-eigenvalue methods for the numerical solution of stiff ordinary differential equations on parallel computers
Order and stability of generalized Padé approximations
Applied Numerical Mathematics
An extension of general linear methods
Numerical Algorithms
On the construction of second derivative diagonally implicit multistage integration methods for ODEs
Applied Numerical Mathematics
Hi-index | 0.00 |
An extension of general linear methods (GLMs), so-called SGLMs (GLMs with second derivative), was introduced to the case in which second derivatives, as well as first derivatives, can be calculated. SGLMs are divided into four types, depending on the nature of the differential system to be solved and the computer architecture that is used to implement these methods. In this paper, we obtain maximal order for two types of SGLMs with Runge-Kutta stability (RKS) property. Also, we construct methods of these types which possess RKS property and A-stability. Efficiency of the constructed methods is shown by numerical experiments.