Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8302Optimal Control in Electrical Heating ProcessesDikusarV VInstitution of Russian Academy of SciencesDorodnicyn Computing Centre of RAS-WojtowiczMPolytechnical Institute-Institution of Russian Academy of SciencesDorodnicyn Computing Centre of RASPolytechnical Institute020220102.212012308092016Copyright © 2010,2010It is suggested an eﬀective numerical and analytical method (NAM) for solving complicated nonlinear multidimensial boundary-value problem of optimal control at interaction of electromagnetic ﬁeld and heat one. NAM is applied for solution parabolic heat equation and also for electromagnetic ﬁeld (elliptical equation). The idea of method is based on approximation nonlinear solution by eigen-function of specially constructed simple linear operator with using smooth properties of inverce one for boundary value problem. The direct methods in space of control are used for solution optimal problem with help of homotopy chain, approximation, forecast and random search. Work was supported by RFBR Grant №09-01-90425,08-01-90101.nonlinear multidimensial boundary-value problemMaxwell equationnumerical and analytical methodoptimal controlparabolic heat equationнелинейные краевые задачиуравнение теплопроводностиуравнение Максвеллаоптимальное управлениечисленно-аналитический методметод введения и возмущения параметровпродолжение решений по параметру