Brunner, Hermann On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods. (English) Zbl 0702.65104 SIAM J. Numer. Anal. 27, No. 4, 987-1000 (1990). 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 Cited in 1 ReviewCited in 67 Documents MSC: 65R20 Numerical methods for integral equations 45G10 Other nonlinear integral equations Keywords:spline collocation methods; nonlinear mixed Volterra-Fredholm integral equation; optimal convergence rates; epidemic PDFBibTeX XMLCite \textit{H. Brunner}, SIAM J. Numer. Anal. 27, No. 4, 987--1000 (1990; Zbl 0702.65104) Full Text: DOI