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


Author: Hermann Brunner
Journal: Math. Comp. 53 (1989), 571-587
MSC: Primary 65R20; Secondary 45D05, 92A15
DOI: https://doi.org/10.1090/S0025-5718-1989-0979936-2
MathSciNet review: 979936
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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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1989-0979936-2
Keywords: Volterra integro-differential equations, infinite delay, Volterra's population equation, spline collocation, implicit Runge-Kutta type methods
Article copyright: © Copyright 1989 American Mathematical Society

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