Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 54, Issue 4, Pages 2640-2663Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1049300
Keywords
integral-algebraic equations of index 2; Volterra integral equations of the first kind; nu-smoothing; tractability index; collocation solutions; optimal order of convergence
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Funding
- National Nature Science Foundation of China [11101130]
- Research Fund of the Heilongjiang Provincial Education Department for the Academic Backbone of the Excellent Young People [1254G044]
- Science and Technology Innovation Team in Higher Education Institutions of Heilongjiang Province [2014TD005]
- Heilongjiang University Science Funds for Distinguished Young Scholars [JCL201303]
- Hong Kong Research Grants Council (GRF HKBU) [200212]
- Natural Sciences and Engineering Research Council of Canada (NSERC) [9406]
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In a previous paper [SIAM J. Numer. Anal., 51 (2013), pp. 2238-2259] we analyzed the optimal orders of convergence of piecewise polynomial collocation solutions for systems of integral-algebraic equations (IAEs) with tractability index mu = 1. The present paper describes the decoupling of systems of IAEs of tractability index mu = 2 and (nu + 1)-smoothing (nu >= 1). It is then shown that the application of the collocation method to the given system of IAEs is equivalent to the application to the decoupled system. While this in principle forms the basis for an elegant analysis of the optimal order of convergence of the method, we show by an example that collocation is not always feasible for general index-2 IAEs. Following the convergence analysis for semiexplicit index-2 IAEs we present two numerical examples: one to verify the predicted orders of convergence and one to show why the collocation method may break down for general IAEs with mu = 2.
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