ISSN:
1572-9125
Keywords:
Mathematics Subject Classification
;
65F15
;
65F30
;
65L20
;
Inverse eigenvalue problem
;
eigenvalue assignment
;
singly-implicit Runge-Kutta method
;
B-stability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The implementation of implicit Runge-Kutta methods requires the solution of large sets of nonlinear equations. It is known that on serial machines these costs can be reduced if the stability function of ans-stage method has only ans-fold real pole. Here these so-called singly-implicit Runge-Kutta methods (SIRKs) are constructed utilizing a recent result on eigenvalue assignment by state feedback and a new tridiagonalization, which preserves the entries required by theW-transformation. These two algorithms in conjunction with an unconstrained minimization allow the numerical treatment of a difficult inverse eigenvalue problem. In particular we compute an 8-stage SIRK which is of order 8 andB-stable. This solves a problem posed by Hairer and Wanner a decade ago. Furthermore, we finds-stageB-stable SIRKs (s=6,8) of orders, which are evenL-stable.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01994850