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Continuous piecewise polynomial collocation methods for generalized auto-convolution Volterra integral equations. (English) Zbl 07714669

Summary: This paper fills a gap in the convergence analysis of collocation solutions in continuous piecewise polynomial space for generalized auto-convolution Volterra integral equations (AVIEs). The solvability of continuous collocation methods is discussed and the uniform boundedness of the collocation solution is provided by a discrete weighted exponential norm. The necessary and sufficient conditions for the optimal global and local (super-) convergence properties of continuous collocation solutions are obtained. Some numerical experiments are given to illustrate the theoretical results.

MSC:

65R20 Numerical methods for integral equations
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References:

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