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

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

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.

Suggested Citation

  • Ashpazzadeh, Elmira & Chu, Yu-Ming & Hashemi, Mir Sajjad & Moharrami, Mahsa & Inc, Mustafa, 2022. "Hermite multiwavelets representation for the sparse solution of nonlinear Abel’s integral equation," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    • Handle: RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002454
    DOI: 10.1016/j.amc.2022.127171
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    References listed on IDEAS

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    1. Zai-Yin He & Abderrahmane Abbes & Hadi Jahanshahi & Naif D. Alotaibi & Ye Wang, 2022. "Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    2. Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    3. Zhu, Li & Wang, Yanxin, 2015. "Numerical solutions of Volterra integral equation with weakly singular kernel using SCW method," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 63-70.
    4. Mohamed R. Ali & Mohamed M. Mousa & Wen-Xiu Ma, 2019. "Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-10, February.
    5. Singh, C.S. & Singh, Harendra & Singh, Somveer & Kumar, Devendra, 2019. "An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1440-1448.
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    1. Muhammad Bilal Khan & Hakeem A. Othman & Michael Gr. Voskoglou & Lazim Abdullah & Alia M. Alzubaidi, 2023. "Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings," Mathematics, MDPI, vol. 11(3), pages 1-23, January.

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