In this paper, the problem seeking solution to the first kind operator equation A u = f is discussed in Sobolev space W 21. By the reproducing kernel of the space W 21, theanalytic solution u(x) of the equation is constructed. It has been shown that the numerical solution un(t) can be obtained directly from the analytic solution, the error can be monotonically decreased in Sobolev norm as the nodes number n increases, furthermore, u (x) converge uniformly to u(x) as the number n tends to infinity.
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