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Based on the state of the problem related to highquality and reliable insulation coating of high-voltage cables, the problems of mathematical modeling of pro-cesses in the loading zone and the delay of the polymer mixture in a single-screw extruder are formulated, which is crucial in terms of providing a high-quality insulation coating. An iterative numerical-analytical method for solving the corresponding nonlinear boundary value problems is proposed, based on the use of finite integral transformations in the spatial and temporal domains and their implementation.
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