Abstract: In, we consider a self-adjoint bounded operator,,, of the form (Formula presented.) It is assumed that is a nonnegative function such that and ; the function is measurable and periodic in all variables, moreover, and. Let,,, be the solution of the Cauchy problem (Formula presented.) where. We show that, for a chosen, the solution converges in, as, to the solution of the homogenized problem (Formula presented.) where and is a positive definite effective matrix. The following error estimate holds: (Formula presented.)