Convergence analysis of the Chebyshev-Legendre spectral method for a class of Fredholm fractional integro-differential equations
Provides a theoretical convergence guarantee for a spectral method applied to a class of fractional integro-differential equations, which is incremental for researchers in numerical analysis.
The authors propose a Chebyshev-Legendre spectral method for solving fractional Fredholm integro-differential equations and prove exponential convergence in L^2-norm, demonstrated through examples with known solutions.
In this paper, we propose and analyze a spectral Chebyshev-Legendre approximation for fractional order integro-differential equations of Fredholm type. The fractional derivative is described in the Caputo sense. Our proposed method is illustrated by considering some examples whose exact solutions are available. We prove that the error of the approximate solution decay exponentially in L^2-norm.