An efficient algorithm (Layered Precise Exponential Method

LPEM）of steady heat conduction equation is presented for Functionally Graded Materials (FGMs) Firstly the steady-state heat conduction equation is discretized equidistantly along the thickness direction with the discrete number M and then is changed into analytic Ordinary Differential Boundary Value Problem (ODBVP) Secondly algebraic equations which have almost no discretization error are established from the ODBVP by using of the precise integral relations of the state parameter between adjacent points

and then the recursion formula for elimination is given from upper algebraic equations The results of Layered Precise Exponential Method have both good accuracy and good efficiency when the function of thermal conductivity is constanttype or exponential

and when the function of thermal conductivity is other forms of continuous and smooth function. The method also applies as long as the layered exponential approximation model is adopted.The numerical examples are presented to demonstrate the effectiveness and reliability of the proposed method.