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To solve the boundary problems for singular ordinary differential equations of the second order the functional-discrete (FD-) method is proposed. The method gives the possibility of obtaining an approximate solution in the numerical-analytical form in the whole half-axis with a guaranteed accuracy. Sufficient conditions of convergence of the method at a rate of a geometrical progression are found. The two-sided approximations are established and an explicit evaluation of the two-sideddoi:10.2478/cmam-2002-0016 fatcat:jxj6j2ua4bc6jjobaqtsjmfy74