Construction and implementation of efficient high-order numerical methods for Volterra integral equations

Volterra integral equations often arise in the mathematical modeling of many technical and natural phenomena with memory. These equations are not simply an isolated small class of functional equations, but they play an important role in time-dependent problems and in many other areas of analysis and applications. In most instances, such equations cannot be solved analytically and one is forced to employ a suitable numerical method that gives an approximation of the exact solution.

Most of the traditional numerical methods for numerically solving Volterra equations are based on classical polynomial interpolation, which are ill-conditioned and lead to Runge's phenomenon if the interpolation nodes are equispaced. This drawback can be overcome by the rather recently developed method of barycentric rational interpolation, and the purpose of this collaboration is to introduce highly accurate and stable schemes based on barycentric rational interpolation for the numerical solution of Volterra equations.