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A perspective on the numerical treatment of Volterra equations. (English) Zbl 0976.65121
Following a short introduction to the basic theory of Volterra integral and integro-differential equations, the author surveys the principle classes of of numerial methods for such functional equations: these include methods based on elementary quadrature formulas; Runge-Kutta type methods; and (exact and discretized) collocation methods. The subsequent discussion of the analysis of these numerical methods focuses on their stability properties. An extensive list of references complements this survey.

MSC:
65R20Integral equations (numerical methods)
45G10Nonsingular nonlinear integral equations
45J05Integro-ordinary differential equations
45E10Integral equations of the convolution type
45D05Volterra integral equations