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(2m+3)[10, 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((2k))(0) = u((2k))(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. (C) 2008 Elsevier B.V. All rights reserved.