Abel's integral operator: sparse representation based on multiwavelets (Q2026366)

The author studies second kind Abel's integral equations through a multiwavelets Galerkin method. The corresponding Abel integral operator is represented upon a sparse matrix, and convergence analysis and numerical simulations are performed. The numerical calculations are deeply simplified by the fact that the decay property of the wavelet coefficients allows the reduction of the number of coefficients in the system of algebraic equations (obtained by the multiwavelets Galerkin method).