Continuous time collocation methods for Volterra-Fredholm integral equations. (English) Zbl 0662.65116

Kauthen, J.-P.

Numer. Math. 56, No. 5, 409-424 (1989).

Second kind integral equations of mixed Volterra-Fredholm type \[ u(x,t)=g(x,t)+\lambda \int^{t}_{0}\int^{b}_{a}K(x,t,\xi,\tau)u(\xi,\tau)d\xi d\tau \] and their nonlinear counterparts arise in various physical and biological problems. We study existence and uniqueness of a solution, continuous time collocation, time discretization and their global and discrete convergence properties.

Reviewer: J.-P.Kauthen

MSC:

65R20	Numerical methods for integral equations
45B05	Fredholm integral equations
45D05	Volterra integral equations

Keywords:

Volterra-Fredholm integral equations; spline collocation; iterated collocation; superconvergence

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