numerical solution of a type of weakly singular nonlinear volterra integral equation by tau method

‎in this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear volterra integral equations with a kernel of the general form s^β(t−s)−^αg(y(s)) based on the tau method‎. ‎in this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎error analysis of this method is also presented‎. ‎some numerical examples are provided to illustrate the accuracy and computational efficiency of the method‎.