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In this paper, an efficient Spectral Collocation method based on the shifted Legen- dre polynomials is applied to study the unsteady boundary-layer flow and heat transfer due to a stretching sheet. A similarity transformation is used to reduce the govern- ing unsteady boundary layer equations to a system of nonlinear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an analytical aproximate solution of this system of nonlinear ordinary differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution proce- dure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed Spectral Collocation method and those of previously published ones.
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