Construction of an Optimal Explicit Difference Formula in the Hilbert Space \(W_{2}^{(3,2)} (0,1)\)

In this paper, an optimal explicit difference formula for any integer k in the Hilbert space W2(3,2)(0, 1) is constructed. Here, an optimal function of the discrete argument is found, which is used to find the optimal error estimate for the explicit difference formula on the class W2(3,2)(0, 1). Furthermore, an optimal error estimate for the explicit difference formula on the class W2(3,2)(0, 1) is calculated. In addition, using the optimal function of the discrete argument, a new formula for the optimal error of explicit difference formulas on the classes W2(m,m−1)(0, 1) is obtained.

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