Abstract
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.
Citation
Yuping Li. Hui Liang. "CONTINUOUS PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR GENERALIZED AUTO-CONVOLUTION VOLTERRA INTEGRAL EQUATIONS." J. Integral Equations Applications 35 (1) 41 - 59, Spring 2023. https://doi.org/10.1216/jie.2023.35.41
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