The floating-point error propagation in the solution of the wave equation by finite differences has been theoretically determined by computing the first moment and the second moment of the round-off error at each time step. Experimental simulations have been carried out for the rounding towards zero arithmetic and the rounding to the nearest arithmetic. The theoretical formulas agree with the experimental results but slightly overestimate them. Experiments have shown that the space order of the finite difference scheme has no noticeable influence on the round-off error of the computed solution. However the choice of parameters such as the time step or the space step can have significant effects on the numerical accuracy of the solution.

Keywords: Floating point arithmetic, numerical error propagation, partial differential equations, finite difference methods