Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-572305220130701Analytic-Approximate Solution For An Integro- Differential Equation Arising In Oscillating Magnetic Fields Using Homotopy Analysis Method518535514138ENH. Saberi-NikDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.S. EffatiDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.R. BuzhabadiDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.Journal Article20100430<span>In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity and efficiency of this method. </span>http://ijo.iaurasht.ac.ir/article_514138_83b91e496581c65b2416ec737b16ac35.pdf