Collocation methods for nonlinear Volterra integro-differential equations with infinite delay

Brunner, Hermann

doi:10.1090/S0025-5718-1989-0979936-2

Collocation methods for nonlinear Volterra integro-differential equations with infinite delay
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Math. Comp. 53 (1989), 571-587 Request permission

Abstract:

In this paper we study the numerical solution of nonlinear Volterra integro-differential equations with infinite delay by spline collocation and related Runge-Kutta type methods. The kernel function in these equations is of the form $k(t,s,y(t),y(s))$, with a representative example given by Volterra’s population equation, where we have $k(t,s,y(t),y(s)) = a(t - s) \cdot G(y(t),y(s))$.

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J. Math. Pures Appl.

Opere Matematiche

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