Hermite multiwavelets representation for the sparse solution of nonlinear Abel's integral equation - Ashpazzadeh, Elmira; Chu, Yu-Ming; Hashemi, Mir Sajjad; Moharrami, Mahsa; İnç, Mustafa (Elsevier Science Inc, 2022)
In this research , we study the numerical solution of the singular Abel's equation of the second kind. Solving this equation is challengeable, because of the nonlinear and singularity. For this purpose, we present an efficient algorithm based on the Galerkin method using biorthogonal Hermite cubic spline multiwavelets (BHCSMWs). Because of the sparse multiscale representations of functions and operators by these wavelets, the CPU time and computer memory are reduced by the proposed algorithm. Also, the convergence analysis of the method is discussed. (C) 2022 Elsevier Inc. All rights reserved.
Keywords: Abel's equation; Caputo fractional derivative; Riemann-Liouville fractional derivative; Biorthogonal Hermite cubic spline scaling