Numerical solution of a nonlinear Abel type Volterra integral equation

We are concerned with the analytical and numerical analysis of a nonlinear weakly singular Volterra integral equation. Owing to the singularity of the solution at the origin, the global convergence order of Euler's method is less than one. The smoothness proper-ties of the solution are investigated and, by a detailed error analysis, we prove that first order of convergence can be achieved away from the origin. Some numerical results are included confirming the theoretical estimates.