منابع مشابه
Exponential Rosenbrock-Type Methods
We introduce a new class of exponential integrators for the numerical integration of large-scale systems of stiff differential equations. These so-called Rosenbrock-type methods linearize the flow in each time step and make use of the matrix exponential and related functions of the Jacobian. In contrast to standard integrators, the methods are fully explicit and do not require the numerical sol...
متن کاملParallel exponential Rosenbrock methods
Exponential Rosenbrock integrators have been shown to be very efficient in solving large stiff differential systems of ODEs. So far, such exponential methods have been derived up to order 5. In this talk we give a convergence result for methods of order up to 6 and construct new integrators of orders 4, 5, and 6. In contrast to the existing schemes of orders 4 and 5, the new schemes, which are ...
متن کاملImplementation of exponential Rosenbrock-type integrators
In this paper, we present a variable step size implementation of exponential Rosenbrock-type methods of orders 2, 3 and 4. These integrators require the evaluation of exponential and related functions of the Jacobian matrix. To this aim, the Real Leja Points Method is used. It is shown that the properties of this method combine well with the particular requirements of Rosenbrock-type integrator...
متن کاملPerturbation results for exponential Rosenbrock-type methods
In this note we consider exponential Rosenbrock-type methods that have been introduced in [1, 2, 3]. Since these methods involve several terms, which can not be computed exactly in praxis it is interesting to understand, how additional errors in the method affect the overall accuracy of the scheme. We will give a perturbation result for general perturbations and study the effect of inexact eval...
متن کاملRosenbrock-type Methods Adapted to Differential-algebraic Systems
We consider the numerical solution of differential-algebraic systems of index one given in Kronecker canonical form. The methods described here are derived from the Rosenbrock approach. Hence, they do not require the solution of nonlinear systems of equations but one evaluation of the Jacobian and one LU decomposition per step. By construction, the s-stage method coincides with a solver for non...
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: ACM Transactions on Mathematical Software
سال: 1982
ISSN: 0098-3500,1557-7295
DOI: 10.1145/355993.355994