An Interval Version of Cauchy's Problem for the Wave Equation
[ 1 ] Instytut Matematyki, Wydział Elektryczny, Politechnika Poznańska | [ P ] employee
2015
paper
english
- Interval Methods
- Finite Difference Method
- Hyperbolic Partial Differential Equations
- Interval Computations
EN The paper is devoted to interval versions of Cauchy’s problem in homogeneous wave equation. The initial condition approximated by the Taylor series of the various orders (as well as with the approximations of the corresponding derivatives) are considered. Interval versions of conventional methods are constructed so as, they contain truncation errors. Truncation errors have been estimated for each interval variant of Cauchy’s condition. All variants were used in solving the wave equation by the central difference interval method. Additionally, all computation have been implemented in floating point interval arithmetic to obtain the solutions, in the form of intervals, which include round-off errors.
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