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A new algorithm based on least-squares method for fractional integro-differential equations
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  • Yuntao Jia,
  • Minqiang Xu,
  • Yingzhen Lin,
  • Danhua Jiang
Yuntao Jia
Beijing Institute of Technology - Zhuhai Campus
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Minqiang Xu
Zhejiang University of Technology

Corresponding Author:[email protected]

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Yingzhen Lin
Beijing Institute of Technology - Zhuhai Campus
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Danhua Jiang
Zhejiang University of Technology
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Abstract

In this paper, a new Legendre orthonormal polynomial–based least–squares method(LSM) is provided for fractional integro-differential equations(FIDEs). We first divide the domain into $n$ cells, and in each cell we apply the least–squares algorithm to obtain an approximating solution. The stability and the optimal convergence order in $W_2^2$–norm error are proven. Numerical examples are studied to verify our theoretical discovery. Comparison with the sextic and eighth $C^{3}-$spline method illustrates that our algorithm can obtain a more accurate approximating solution.