Advantages of the Discrete Stochastic Arithmetic to Validate the Results of the Taylor Expansion Method to Solve the Generalized Abel’s Integral Equation

The aim of this paper is to apply the Taylor expansion method solve first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: FPA DSA. In order DSA, we use CESTAC CADNA library. Using method, can find optimal step approximation, error, some numerical instabilities. They are novelties DSA in comparison FPA. error analysis proved. Furthermore, theorem presented. a new termination criterion instead traditional absolute error. Several examples approximated based results show applications advantages than