Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis
AIMS MATHEMATICS(2024)
摘要
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.
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关键词
Legendre-Gauss-Lobatto,fractional Fredholm integro-di ff erential equation,Caputo,fractional derivative,convergence analysis,spectral method,image processing [1],dynamical system control theory,signal processing,electrical networks,optics
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