Numerical method for estimating the growth rate of the rounding error in uniform metric

A numerico-analytical algorithm for estimating the rounding errors in the uniform metric is developed. Their boundedness is established over the entire range of calculating the current-voltage characteristics of long Josephson junctions using the proposed second-order scheme. For a system of two difference equations as an example, it is shown how the growth rate of rounding errors in the uniform metric can be analyzed numerically in the case of a power-law instability. In addition, estimates are obtained for the growth rate of the rounding errors in the uniform metric for the third-order Rusanov scheme. The calculations were carried out on the Govorun supercomputer using the REDUCE system.