Use of Legendre multiwavelets to solve Carleman type singular integral equations
Applied Mathematical Modelling
This paper is concerned with obtaining approximate numerical solutions of Carleman type singular integral equations by using Legendre multiwavelet basis. The properties of Legendre multiwavelets are first given and the low- and high-pass filters for two-scale relations involving Legendre multiwavelets have been derived. The scheme proposed here consists of two basic steps. In the first step the multiscale representation of the given integral operator is obtained and explicit expressions for the elements of the matrix associated with the multiscale representation are derived. In the second step the given integral equation is converted into a system of linear algebraic equations. The convergence of the method is proved in L2 space. Two illustrative examples from elasticity are given to show the efficiency of the method developed here.
Paul, Swaraj; Panja, M. M.; and Mandal, B. N., "Use of Legendre multiwavelets to solve Carleman type singular integral equations" (2018). Journal Articles. 1460.