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In view of the Economic Class of two-dimensional partial differential equation, a two dimensional scale function was chosen and was applied to the wavelet collocation method. Simultaneously, the two dimensional scaling basis function was proved satisfy the interpolate property. And according to two dimensional multi-resolution analysis theory, the approximate formulas of solutions for the Economic Class of the two dimensional differential equations were given. The two dimensional partial differential equations were separated by the wavelet collocation method and the system of ordinary differential equations was built. At last, the system of partial differential equations was solved. The result was better than the traditional Galerkin method and with higher precision. 2-D Shannon wavelet collocation method Supposed the monadic function ( ) x φ to produce multi-resolution analysis, but the monadic function ( ) y φ produces another multi-resolution analysis, then 1 j V and 2 j V tensor product accumulates the space with the 2 1 j j j V V V ⊗ = Because the basis of 1 j V was ( ) { } 2 j x k φ − − ,but the basis of 2 j V is ( ) { } 2 j y l φ − − ,so the basis of j V was ( ) ( ) 2 2 j j x k y l φ φ − − − ⋅ − .The bivar function ( ) y x f , may be introduced the symbol ( ) ( ) , , , 2 , 2 j j j k l f x y f x k y l − − = − − Recording ( ) ( ) ( ) , x y x y φ φ φ = ⋅ so ( ) { } , , , ; , j k l x y k l Z φ ∈ was the basic of j V Then { } j V forms a multi-resolution analys was in ( ) R R L × 2 .But ( ) , x y φ was the corresponding scale function, take the Shannon scale function as the example, namely ( ) ( ) ( ) sin sin , x y x y x y x y π π φ φ φ π π = ⋅ = ⋅ The Figure 1. was produced by the tensor product of the two-dimensional Shannon scale function. Fig1. 2-D Shannon scale function 1 National Social Science Fund project (11BJY080) 、(14BJL032)and National Science Foundation project (71340022)、Heilongjiang Province philosophy of social science projects (13B024) and Heilongjiang Provincial Department of Education Project (12541190). International Industrial Informatics and Computer Engineering Conference (IIICEC 2015) © 2015. The authors Published by Atlantis Press 526 1.1. The structure of basis function and its characteristic Considering the two-dimensional function ( ) y x f , ,and taking the two-dimensional Shannon scale function to as the basis function, Because the situation of evenly discrete was more convenient than the noneven discrete. Therefore according to the multi-resolution analysis theory to the function ( ) y x f , in its definition domain[0 , ] [0 , ] l l × ( ) 0 l > to carry on the even discrete., and the unit grid size records for j l 2 = ∆ ( j was suitable integer), ∆ = m x m , j m 2 1 0 , , , = ∆ = n y n , j n 2 1 0 , , , = Definition basis function was ( ) ( ) ( ) ( ) ( ) , , sin sin , m n j m n m n x x y y w x y x x y y π π π π − − ∆ ∆ = ⋅ − − ∆ ∆ Meanwhile ( ) ( ) ( ) sin k j k k x x w x x x x π π − ∆ − = − ∆ Theory 1.1. The basis function was satisfied the following properties: 1. Interpolation ( ) j i k ik w x x δ − = 2. Orthogonality j i j k ik w x x w x x dx δ +∞ −∞ − − = ∆ ∫ ( ) ( ) 3. Regeneration For any positive integer n satisfing

The Wavelet Collocation Method Based on Economic Class of Equations Shannon