A minimal search method for solving fractional integro-differential equations based on modified Legendre multiwavelets

Wu, Longbin; Chen, Zhong; Ding, Xiaohua

doi:10.1007/s12190-021-01573-2

Cited by 3 publications

(1 citation statement)

References 29 publications

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“…The main feature of using orthogonal functions is that they reduce dynamical system problems to those of solving a system of algebraic equations using differentiation or integration operational matrices. Special attention has been given to applications of the block pulse functions [38,39], spline wavelets [40], Legendre wavelets [41,42], Chebyshev polynomials [43,44], Walsh functions [45], and wavelet collocation method [46].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Fractional Integro-Differential Equations Via Fourth-Degree Hat Functions

Mohammed

Khudair

2023

ijcsm

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The goal of this paper is to construct new fourth-degree hat functions (FDHFs) and study their properties in order to develop a new numerical method for solving fractional integro-differential equations. The equation under consideration is transformed into a set of algebraic equations by using FDHFs, which makes it simple to solve the system using one of the iterative methods. In fact, this method’s advantage was that it was easy to use and had fifth-order convergence, as we showed in the section on error analysis. The numerical results demonstrate that the new technique works well through the presented examples.

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Section: Introductionmentioning

confidence: 99%

Numerical Solution of Fractional Integro-Differential Equations Via Fourth-Degree Hat Functions

Mohammed

Khudair

2023

ijcsm

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An efficient numerical algorithm for solving nonlinear fractional Volterra integro-differential equation

Dai,

Guan,

Niu

2024

Comp. Appl. Math.

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Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis

Tedjani,

Amin,

Abdel-Aty

et al. 2024

MATH

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<abstract><p>The main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main idea is to use Caputo derivatives and Legendre-Gauss interpolation for nonlinear FFIDEs. A rigorous convergence analysis is provided and confirmed by numerical tests. In addition, we provide some numerical test cases to demonstrate that the approach can preserve the non-smooth solution of the underlying problem.</p></abstract>

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A minimal search method for solving fractional integro-differential equations based on modified Legendre multiwavelets

Cited by 3 publications

References 29 publications

Numerical Solution of Fractional Integro-Differential Equations Via Fourth-Degree Hat Functions

Numerical Solution of Fractional Integro-Differential Equations Via Fourth-Degree Hat Functions

An efficient numerical algorithm for solving nonlinear fractional Volterra integro-differential equation

Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis

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