<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si78.svg"><mml:mrow><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>-spline for solution of second order fractional integro-differential equations

Mohammadizadeh, S.; Rashidinia, Jalil; Ezzati, Reza; Khumalo, M.

doi:10.1016/j.aej.2020.07.011

Cited by 5 publications

(2 citation statements)

References 30 publications

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“…The RMS errors obtained by our presented method are compared with the eighth C 3 −spline method proposed in [8] in Table 1. Numerical results illustrate that our method can obtain a more accurate solution.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Jumana proposed an operational matrix method for FDEs by using the generalized Gegenbauer-Humbert polynomials in [4]. Besides, several numerical methods, including Taylor expansion methods, homotopy perturbation methods, collocation methods, reproducing kernel collocation methods and C 3 −spline methods are proposed in [5]- [8] for solving FIDEs.…”

Section: Introductionmentioning

confidence: 99%

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A new algorithm based on least-squares method for fractional integro-differential equations

Jia,

Xu,

Lin

et al. 2024

Preprint

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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.

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Section: Numerical Examplesmentioning

confidence: 99%