Hermite multiwavelets representation for the sparse solution of nonlinear Abel's integral equation

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.

Automated summary

In this research, we focus on the numerical solution of the singular Abel's equation of the second kind. A challenging task due to its nonlinearity and singularity. To address this issue, an efficient algorithm based on the Galerkin method using biorthogonal Hermite cubic spline multiwavelets (BHCSMWs) is proposed. The proposed algorithm reduces the CPU time and computer memory usage by taking advantage of the sparse multiscale representations of functions and operators provided by these wavelets. The convergence analysis of the method is also discussed.