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

Elmira Ashpazzadeh, Yu-Ming Chu, Mir Sajjad Hashemi, Mahsa Moharrami and Mustafa Inc

Applied Mathematics and Computation, 2022, vol. 427, issue C

Abstract: 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.

Keywords: Abel’s equation; Caputo fractional derivative; Riemann–Liouville fractional derivative; Biorthogonal Hermite cubic spline scaling (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002454

DOI: 10.1016/j.amc.2022.127171

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