The Peculiarity of the Numerical Differentiation of One and Two Dimension Functions Based on the New Class of Wavelets

The Peculiarity of the Numerical Differentiation of One and Two Dimension Functions Based on the New Class of Wavelets. V.F. Kravchenko, A.V. Yurin

The new method of the numerical differentiation based on the wavelets is considered. Owing to the application of the connection coefficients for the first-order derivative, the rigorous proof of the method is produced. They are represented as the integral of multiplication either of the wavelet or the scaling function on itself derivative. The connection coefficients are weight sequence for symmetrical finite-difference operator DJ with the step of 2-J. The precision of it depends on scale J. A wide range of differential operators on the basis of classical wavelets (such as Meyer-s, Doubechies-s, Coifman-s) and new Kravchenko wavelets are considered. The high calculation accuracy of derivative on the basis of finite-difference operators with weight sequence on the basis of new wavelets is examined with the help of the definite examples of differentiation of one and two dimension functions.