The tolerance proportionality of adaptive ODE solvers
نویسندگان
چکیده
منابع مشابه
Dynamical Systems and Adaptive Timestepping Ode Solvers
Initial value problems for ODEs are often solved numerically using adap-tive timestepping algorithms. We formulate a large class of such algorithms as discrete dynamical systems which are discontinuous and of higher dimension than the underlying ODE. By assuming suuciently strong nite-time convergence results on some neighbourhood of an attractor of the ODE we prove existence and upper semicont...
متن کاملThe Effective Stability of Adaptive Timestepping ODE Solvers
Abstract. We consider the behaviour of certain adaptive timestepping methods, based upon embedded explicit Runge-Kutta pairs, when applied to dissipative ODEs. It has been observed numerically that the standard local error controls can impart desirable stability properties, but this has only been rigorously verified for very special, low-order, Runge-Kutta pairs. The rooted-tree expansion of a ...
متن کاملSimple ODE Solvers - Error Behaviour
y(t0) = y0 Here f(t, y) is a given function, t0 is a given initial time and y0 is a given initial value for y. The unknown in the problem is the function y(t). Two obvious considerations in deciding whether or not a given algorithm is of any practical value are (a) the amount of computational effort required to execute the algorithm and (b) the accuracy that this computational effort yields. Fo...
متن کاملSimple ODE Solvers - Error Behaviour
y(t0) = y0 Here f(t, y) is a given function, t0 is a given initial time and y0 is a given initial value for y. The unknown in the problem is the function y(t). Two obvious considerations in deciding whether or not a given algorithm is of any practical value are (a) the amount of computational effort required to execute the algorithm and (b) the accuracy that this computational effort yields. Fo...
متن کاملParallel ODE solvers based on block BVMs
In this paper we deal with Boundary Value Methods (BVMs), which are methods recently introduced for the numerical approximation of initial value problems for ODEs. Such methods, based on linear multistep formulae (LMF), overcome the stability limitations due to the well-known Dahlquist barriers, and have been the subject of much research in the last years. This has led to the definition of a ne...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1993
ISSN: 0377-0427
DOI: 10.1016/0377-0427(93)90277-i