(A) hermite collocation method for the abel integral equations using transformation

Abstract

The solution of the Abel Volterra integral equations has, in general, unbounded derivatives at the endpoint of the interval of integral. Under certain transformation of Abel Volterra integral equations, the transformed solution has bounded derivatives at the endpoint. In this thesis, we apply a Hermite collocation methods to the transformed Abel-Volterra integral equations. The method is shown to be convergent $N^{-4}$, where N is mesh size. Many numerical examples are included and numerical data have been generated to confirm our findings.