Wavelet based numerical method for solving fractional integro-differential equation with a weakly singular kernel

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integrodi erential equation (FIDE) with a weakly singular kernel. First, a collocation method based on Haar wavelets (HW), Legendre wavelet (LW), Chebyshev wavelets (CHW), second kind Chebyshev wavelets (SKCHW), Cos and Sin wavelets (CASW) and BPFs are presented for driving approximate solution FIDEs with a weakly singular kernel. Error estimates of all proposed numerical methods are given to test the convergence and accuracy of the method. A comparative study of accuracy and computational time for the presented techniques is given.