2015/09/08 by V. S. Sizikov, Sizikov, Valery, Denis Sidorov +1
Mathematics · Physics and Astronomy · Engineering · #Numerical methods in inverse problems #Electromagnetic Scattering and Analysis #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.1509.02586
We propose the generalized quadrature methods for numerical solution of\nsingular integral equation of Abel type. We overcome the singularity using the\nanalytical calculation of the singular integral expression. The problem of\nsolution of singular integral equation is reduced to nonsingular system of\nlinear algebraic equations without shift meshes techniques employment. We also\npropose generalized quadrature method for solution of Abel equation using the\nsingular integral. Relaxed errors bounds are derived. In order to improve the\naccuracy we use Tikhonov regularization method. We demonstrate the efficiency\nof proposed techniques on infrared tomography problem. Numerical experiments\nshow that it make sense to apply regularization in case of highly noisy sources\nonly. That is due to the fact that singular integral equations enjoy\nselfregularization property.\n