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Numerical solutions of a hyperbolic differential-integral equation. (English) Zbl 0651.65099

This paper deals with the approximate solution of partial integro- differential equations of the form \[ \partial u/\partial a+\partial u/\partial t=-d(\int^{T}_{0}u(s,t)ds)\cdot u,\quad u(0,t)=g(t),\quad u(a,0)=\alpha (a), \] where d, g and \(\alpha\) are given smooth functions, with d nonnegative. The numerical method is based on the method of lines, employing discretization in time and the trapezoidal rule for the integral term. Various aspects of the detailed convergence analysis are illustrated by numerical examples, and extensions to more general partial integro-differential equations (arising in the mathematical modelling of the age structure of a given population) are indicated.
Reviewer: H.Brunner

MSC:

65R20 Numerical methods for integral equations
92D25 Population dynamics (general)
45K05 Integro-partial differential equations
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References:

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