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Two-dimensional Legendre wavelets and operational matrices of integration. (English) Zbl 1092.65021

Summary: One-dimensional Legendre wavelets are the basis of a numerical method for solving one-dimensional variational problems and integral equations. In this paper we introduce two-dimensional Legendre wavelets. These wavelets are defined over the interval \([0,1]\times[0,1]\) and an orthonormal set over this interval. The integration of the product of two-dimensional Legendre wavelets over \([0,1]\times[0,1]\) is equal one. We compute operational matrices of integration for two-dimensional Legendre wavelets. These operational matrices are suitable tools for two-dimensional problems. Two-dimensional Legendre wavelets are a numerical method for solving two-dimensional variational problems.

MSC:

65D32 Numerical quadrature and cubature formulas
65T60 Numerical methods for wavelets
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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