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Applicability of spline collocation to cordial Volterra equations. (English) Zbl 1266.65208

The authors discuss the applicability of spline collocation to cordial Volterra equations. First, the authors formulate some applicability condition for \(m=2\) using the basis \({1,t}\) of \(\mathfrak{P_{1}}\) instead of Lagrange basis. Later, the authors apply their results to some concrete cordial equations including the Abel equation. Finally, they comment on the numerical check of the applicability condition for different vales of \(m\) and present some illustrative numerical examples.

MSC:

65R20 Numerical methods for integral equations
45A05 Linear integral equations
45D05 Volterra integral equations
45E99 Singular integral equations