ISSN:
1572-9125
Keywords:
AMS(MOS): 65L05
;
Second order initial value problems
;
region of absolute stability
;
interval of periodicity
;
interval of (weak) stability
;
superstable methods
;
implicit Runge-Kutta methods
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Using the well known properties of thes-stage implicit Runge-Kutta methods for first order differential equations, single step methods of arbitrary order can be obtained for the direct integration of the general second order initial value problemsy″=f(x, y, y′),y(x o)=y o,y′(x o)=y′ o. These methods when applied to the test equationy″+2αy′+β 2 y=0, α,β≥0, α+β〉0, are superstable with the exception of a finite number of isolated values ofβh. These methods can be successfully used for solving singular perturbation problems for which δf/δy and/or δf/δy′ are negative and large. Numerical results demonstrate the efficiency of these methods.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02219237
Permalink