A spectral approach to non-linear weakly singular fractional integro-differential equations

被引:4
|
作者
Faghih, Amin [1 ]
Rebelo, Magda [2 ,3 ]
机构
[1] Sahand Univ Technol, Fac Basic Sci, Dept Appl Math, Tabriz, Iran
[2] FCT NOVA, Ctr Math & Applicat NovaMath, P-2829516 Caparica, Portugal
[3] FCT NOVA, Dept Math, P-2829516 Caparica, Portugal
关键词
Weakly singular fractional integro-differential equation; Caputo derivative operator; Generalized Jacobi polynomials; Spectral Petrov-Galerkin method; Convergence; NUMERICAL-SOLUTION; TAU METHOD; SYSTEMS;
D O I
10.1007/s13540-022-00113-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, a class of non-linear weakly singular fractional integro-differential equations is considered, and we first prove existence, uniqueness, and smoothness properties of the solution under certain assumptions on the given data. We propose a numerical method based on spectral Petrov-Galerkin method that handling to the non-smooth behavior of the solution. The most outstanding feature of our approach is to evaluate the approximate solution by means of recurrence relations despite solving complex non-linear algebraic system. Furthermore, the well-known exponential accuracy is established in L-2-norm, and we provide some examples to illustrate the theoretical results and the performance of the proposed method.
引用
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页码:370 / 398
页数:29
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