On the representation of the differential operator in bases of periodic coiflets and it's application

  • Authors:

  • Anna Deytseva

  • Affiliations:

  • Grodno State University, Grodno, Belarus

  • Venue:
  • CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
  • Year:
  • 2007

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Abstract

In the present paper multiresolutional representation of differential operator in basis of periodized coiflets was constructed. The properties of differential operator coefficients have been investigated. Taking into consideration the behavior of Coifman scaling function, in considered multiresolutional representation of differential operator, coefficients of wavelet-approximation are substituted by evaluations of the function at dyadic points. For sufficiently smooth function the convergence rate of the considered approximations to derivative is stated. For 1-periodic function the formula of numeric differentiation is obtained, and also the error estimate is stated. The application of multiresolution representation of differential operator for numerical solution of ordinary differential equation with periodic boundary conditions is considered.