The dynamic time warping (DTW) is a widely-used method that allows us to efficiently compare two time series that can vary in speed. Given two strings A and B of respective lengths m and n, there is a fundamental dynamic programming algorithm that computes the DTW distance for A and B together with an optimal alignment in time and space. In this paper, we tackle the problem of interactive computation of the DTW distance for dynamic strings, denoted, where character-wise edit operation (insertion, deletion, substitution) can be performed at an arbitrary position of the strings. Let M and N be the sizes of the run-length encoding (RLE) of A and B, respectively. We present an algorithm for that occupies space and uses time to update a compact differential representation of the DP table per edit operation, where denotes the number of cells in whose values change after the edit operation. Our method is at least as efficient as the algorithm recently proposed by Froese et al. running in time, and is faster when is smaller than which, as our preliminary experiments suggest, is likely to be the case in the majority of instances.