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Collocation methods for pantograph-type Volterra functional equations with multiple delays. (English) Zbl 1153.65123
The author analyzes the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integro-differential equations with multiple (vanishing) proportional delays $$\theta _{j}(t) = q_{j}t$$ $$(0<q_{1}< \cdots < q_{r} < 1)$$. It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true. It is suggested to try Adomian decomposition method for solving such kinds of equations and to compare with collocation technique.

##### MSC:
 65R20 Numerical methods for integral equations 34K06 Linear functional-differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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