I cannot do much to shorten and simplify it, but I think this is a little clearer with a few unnecessary words eliminated: As seen in Figure 3, the method generates numerical solutions at three equidistant points simultaneously. The solutions at points w(1), w(2) and w(3) in the current block are obtained by subsuming the solutions from the previous block , which are the points w(-3) through w(0). After calculating the solutions in the current block, the process advances to the next blocks until it reaches the end of the interval.
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