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We first introduce some related definitions of the bounded linear operator L in the reproducing kernel space W 2 m(D). Then we show spectral analysis of L and derive several property theorems.

We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that then-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.