Study on interval Volterra integral equations via parametric approach of intervals

This work investigates the interval Volterra integral equation (IVIE) and its solution techniques through the parametric representation of intervals. First, the general form of the second-kind IVIE is expressed in both lower-upper bound format and its equivalent parametric form. Next, the methods of successive approximations and resolvent kernel are developed to solve the IVIE, utilizing parametric approaches and interval arithmetic. The solutions are presented in both parametric and lower-upper bound representations. Lastly, a series of numerical examples are provided to illustrate the application of these methods.