We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L^∞ norm and weighted L^2-norm. The numerical examples are given to illustrate the theoretical results.
A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind.We provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-norm and L¥-norm will decay exponentially provided that the kernel function is sufficiently smooth.Numerical results are presented,which confirm the theoretical prediction of the exponential rate of convergence.
