Abstarct: In this thesis, The optimal control problem considered here is associated to the minimization of the tracking functional subject to parabolic equations is examined. At first, in chapter 1 the corresponding optimality system of the origional problem is first given. In chapters 2-5 Cubic, Quartic, Quintic and Septic B- spline collocation methods that solves parabolic distributed optimality system, are then investigated. The end of chapter, accuracy properties of Cubic, Quartic, Quintic and Septic Bspline collocation methods are showed by using several numerical simulations, that the resulting scheme also shows robustness with respect to changes of the value of cost of the control, is sufficiently small. Note that we have computed the numerical results by Matlab programming.