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Numerical implementation of nonlinear system of fractional Volterra integral–differential equations by Legendre wavelet method and error estimation
Author(s) -
Shen Lijing,
Zhu Shuai,
Liu Bingcheng,
Zhang Zirui,
Cui Yuanda
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22582
Subject(s) - legendre wavelet , mathematics , legendre polynomials , algebraic equation , wavelet , nonlinear system , volterra integral equation , associated legendre polynomials , mathematical analysis , integral equation , wavelet transform , discrete wavelet transform , orthogonal polynomials , gegenbauer polynomials , computer science , classical orthogonal polynomials , physics , quantum mechanics , artificial intelligence
In the current study, a numerical scheme for solving the nonlinear system of fractional Volterra integro‐differential equations via Legendre wavelet is proposed. The Legendre wavelet operational matrix of fractional integration is derived and utilized to alter the main system to a system of algebraic equations. In addition, the error estimate of the original system is investigated in detail. Lastly, several numerical examples are set forth to test the proposed method and the obtained numerical results are compared with those from the CAS wavelet method.