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This article examines the development of operator splitting methods in Soviet numerical analysis during 1955–1975, with particular focus on N.N. Yanenko’s formalization of the Method of Fractional Steps at the Siberian Branch of the USSR Academy of Sciences. While similar techniques were independently developed in the West (Peaceman-Rachford 1955, Douglas-Rachford 1956), the Soviet school pursued a distinct trajectory shaped by acute hardware constraints and deep epistemological commitments to operator theory. Through analysis of technical publications, archival materials, and comparative historiography, this study argues that material scarcity catalyzed a systematic research program emphasizing computational economy, while a pre-existing mathematical culture valorizing theoretical elegance reinforced this trajectory. The case illuminates how geopolitical constraints and intellectual traditions jointly shaped algorithmic innovation, contributing to methods that ironically became foundational for modern massively parallel computing. Significant archival gaps limit definitive claims about industrial applications, highlighting the need for further primary source research.