On a Method for Constructing Optimal Difference Formulas Using Discrete Operators with Variable Coefficients

This paper deals with the problem of constructing optimal difference formulas in the Hilbert space H2m0,1 through Sobolev’s method. Firstly, Sobolev’s method of construction of optimal difference formulas in the Hilbert space H2m0,1, which is based on the discrete analogue Lhβ, is described. Secondly, a discrete analogue Lhβ of differential operator d2dx2+2sgnxddx+11−d2dx2m−2 having variable coefficients is contructed. Thirdly, for m=2 the optimal difference formula is obtained. Finally, at the end of the paper, we present some numerical results, which serves to confirm the numerical convergence of the optimal difference formula.

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