Cr-LOHNER ALGORITHM

نویسندگان

  • Daniel Wilczak
  • Piotr Zgliczyński
چکیده

We present a Lohner type algorithm for the computation of rigorous bounds for the solutions of ordinary differential equations and its derivatives with respect to the initial conditions up to an arbitrary order.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

C-Lohner algorithm

We present a C-Lohner algorithm for computation of rigorous bounds for solutions of ordinary differential equations.

متن کامل

A Lohner-type Algorithm for Control Systems and Ordinary Differential Inclusions

We describe a Lohner-type algorithm for the computation of rigorous upper bounds for reachable set for control systems, solutions of ordinary differential inclusions and perturbations of ODEs.

متن کامل

Geometric Series Bounds for the Local errors of Taylor Methods for Linear n-th-Order ODEs

Interval Taylor methods for the validated solution of initial value problems for ODEs were introduced by Moore (1965a, 1965b, 1966). Lohner (1987, 1988, 1992) developed a comprehensive software package of an advanced interval Taylor method, which he applied successfully to many linear and nonlinear problems. But, as Lohner (1988) remarked, the step size of his method is limited by the step size...

متن کامل

ar X iv : 0 70 4 . 07 20 v 1 [ m at h . N A ] 5 A pr 2 00 7 C r - Lohner algorithm

We present a Lohner type algorithm for the computation of rigorous bounds for solutions of ordinary differential equations and its derivatives with respect to initial conditions up to arbitrary order. As an application we prove the existence of multiple invariant tori around some elliptic periodic orbits for the pendulum equation with periodic forcing and for Michelson system.

متن کامل

Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs

We describe a Lohner-type algorithm for rigorous integration of dissipative PDEs. Using it for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions we give a computer assisted proof the existence of multiple periodic orbits.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012