Title of article :
an interval version of the kuntzmann-butcher method for solving the initial value problem
Author/Authors :
marciniak, andrzej poznan university of technology - institute of computing science, poznan, poland , marciniak, andrzej higher vocational state school in kalisz poznanska - department of computer science, kalisz, poland , szyszka, barbara poznan university of technology - institute of mathematics, poznan, poland , hoffmann, tomasz poznan supercomputing and networking center, poznan, poland
Abstract :
the kutzmann-butcher method is the unique implicit four-stage runge-kutta method of order 8. in many problems in ordinary differential equations this method realized in oating-point arithmetic gives quite good approximations to the exact solutions, but the results obtained do not contain any information on rounding errors, representation errors and the error of the method. thus, we describe an interval version of this method, which realized in oating-point interval arithmetic gives approximations (enclosures in the form of an interval) containing all these errors. the described method can also include data uncertainties in the intervals obtained.
Keywords :
initial value problem , runge , kutta methods , kuntzmann , butcher method , interval runge , kutta methods , floating , point interval arithmetic
Journal title :
Computational Methods for Differential Equations
Journal title :
Computational Methods for Differential Equations
