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

被引：49

作者：

Ashpazzadeh, Elmira ^{[1
]}

Chu, Yu-Ming ^{[2
,3
]}

Hashemi, Mir Sajjad ^{[1
]}

Moharrami, Mahsa ^{[1
]}

Inc, Mustafa ^{[4
,5
,6
]}

机构：

[1] Univ Bonab, Basic Sci Fac, Dept Math, POB 55513-95133, Bonab, Iran

[2] Hangzhou Normal Univ, Inst Adv Study Honroing Chen Jian Gong, Hangzhou 311121, Peoples R China

[3] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China

[4] Biruni Univ, Dept Comp Engn, Istanbul, Turkey

[5] Firat Univ, Sci Fac, Dept Math, TR-23119 Elazig, Turkey

[6] China Med Univ, Dept Med Res, Taichung, Taiwan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2022年 / 427卷

关键词：

Abel's equation; Caputo fractional derivative; Riemann-Liouville fractional derivative; Biorthogonal Hermite cubic spline scaling; HILBERT-SPACE METHOD; NUMERICAL-SOLUTION; DIFFERENTIAL-EQUATIONS; APPROXIMATE SOLUTION; CONSTRUCTION;

D O I：

10.1016/j.amc.2022.127171

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：16

共 46 条

[1] A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems [J].

Abbasbandy, Saeid ;

Azarnavid, Babak ;

Alhuthali, Mohammed S. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 :293-305

[2] Group preserving scheme and reproducing kernel method for the Poisson-Boltzmann equation for semiconductor devices [J].

Akgul, Ali ;

Inc, Mustafa ;

Hashemi, Mir Sajjad .

NONLINEAR DYNAMICS, 2017, 88 (04) :2817-2829

[3] Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method [J].

Ali, Mohamed R. ;

Mousa, Mohamed M. ;

Ma, Wen-Xiu .

ADVANCES IN MATHEMATICAL PHYSICS, 2019, 2019

[4]

[Anonymous], 1999, MATH SCI ENG

[5]

[Anonymous], 2006, Science

[6] Biorthogonal multiwavelets on the interval for solving multidimensional fractional optimal control problems with inequality constraint [J].

Ashpazzadeh, Elmira ;

Lakestani, Mehrdad ;

Yildirim, Ahmet .

OPTIMAL CONTROL APPLICATIONS & METHODS, 2020, 41 (05) :1477-1494

[7] Biorthogonal multiwavelets on the interval for numerical solutions of Burgers' equation [J].

Ashpazzadeh, Elmira ;

Han, Bin ;

Lakestani, Mehrdad .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 317 :510-534

[8] Numerical solution of a modified anomalous diffusion equation with nonlinear source term through meshless singular boundary method [J].

Aslefallah, Mohammad ;

Abbasbandy, Saeid ;

Shivanian, Elyas .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2019, 107 :198-207

[9] NUMERICAL-SOLUTION OF AN ABEL INTEGRAL-EQUATION BY A PRODUCT TRAPEZOIDAL METHOD [J].

ATKINSON, KE .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1974, 11 (01) :97-101

[10] EXISTENCE THEOREM FOR ABEL INTEGRAL-EQUATIONS [J].

ATKINSON, KE .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1974, 5 (05) :729-736

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