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An integrodifferential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The local polynomial regression method (LPR) is used to solve this equation. The reliability of this method and the reduction in the size of computational domain give this method a wider applicability. Several representative examples are given to reconfirm the efficiency of these algorithms. The results of applying this theory to the integro-differential equation with time-periodic coefficients reveal that LPR method possesses very high accuracy, adaptability, and efficiency.