Solving singular boundary-value problems of higher even-order

In this paper,we present a new algorithm to solve a kind of singular boundary-value problems of higher even-order based on the theory of numerical analysis in the reproducing kernel space W 2 2 m + 3 [ 0 , 1 ] . Singular boundary-value problem of sixth-order has been discussed for the problem { u ( 6 ) ( x ) + a ( x ) u ( 4 ) ( x ) + b ( x ) u ″ ( x ) + c ( x ) u ( x ) = f ( x ) , 0 < x < 1 u ( 2 k ) ( 0 ) = u ( 2 k ) ( 1 ) = 0 , 0 ≤ k ≤ 2 , in the case of m = 2 . The numerical results are compared with both the exact solution and its n -order ( n = 1 , 2 , … , 6 ) derived functions in the example. It is demonstrated that our method is of high precision and significance.