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On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods. (English) Zbl 0702.65104

Continuous- and discrete-time collocation methods are considered for the numerical solution of the nonlinear mixed Volterra-Fredholm integral equation \((*)\quad u(t,x)=f(t,x)+\int^{t}_{0}\int_{\Omega}k(t,\tau,x,\xi,u(\tau,\xi))d\;xi d\tau.\) The optimal convergence rates of these methods are investigated. Problems of type (*) arise in the mathematical modeling of the spatio-temporal development of an epidemic.
Reviewer: E.Hairer

MSC:

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