Time-stepping methods for Volterra-Fredholm integral equations

Abstract

The semidiscretization in space of Volterra-Fredholm integral equations (arising, for example, as mathematical models of the spreading of epidemics) leads to large systems of Volterra integral equations. Here, we study inexpensive timestepping methods using certain DQ (= direct quadrature) methods which are employed in a way that exploits the local superconvergence properties of spatial collocation. The performance of these methods is then compared with that of time-stepping based on collocation methods.

Keywords

• volterra-fredholm integral equations
• spline collocation methods
• direct quadrature methods