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Time-stepping methods for Volterra-Fredholm integral equations. (English) Zbl 1095.65117
Summary: 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 time-stepping methods using certain 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.

MSC:
65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
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