A central-backward difference interval method for solving the wave equation
[ 1 ] Instytut Informatyki, Wydział Informatyki, Politechnika Poznańska | [ 2 ] Instytut Matematyki, Wydział Elektryczny, Politechnika Poznańska | [ P ] employee
2013
paper
english
- wave equation
- PDE
- difference method
- initial-boundary value problem
- floating-point interval arithmetic
- interval methods
EN The paper is devoted to an interval difference method for solving one dimensional wave equation with the initial-boundary value problem. The method is an adaptation of the well-known central and backward difference methods with respect to discretization errors of the methods. The approximation of an initial condition is derived on the basis of expansion of a third-degree Taylor polynomial. The initial condition is also written in the interval form with respect to a discretization error. Therefore, the presented interval method includes all approximation errors (of the wave equation and the initial condition). The floating-point interval arithmetic is used. It allows to obtain interval solutions which contain all calculations errors. Moreover, it is indicated that an exact solution belongs to the interval solution obtained.
518 - 527
WoS (15)