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Legendre wavelet for solving supersingular integral. (Chinese. English summary) Zbl 1265.42111

Summary: Numerical methods of supersingular integrals are an important topic. Based on the definition of a Hadamard finite-part integral of the supersingular integral we give a method which calculates the supersingular integral by using Legendre wavelets. When the singular point is located in the interval, since a Legendre wavelet has better orthogonality, good explicit expression and computability of the wavelet function, we can convert the singular point of interval into the endpoint of interval. Then, by making use of the definition of the Hadamard finite-part integral where the singular point is located at the endpoint of the interval, we can compute the \((p+1)\)st order supersingular integral, where \(p\in \mathbb{N}^+\). Finally, the feasibility and validity of the method are proved by examples.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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