Orthogonal collocation for a nonlinear integro-differential equation |
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| Authors: | Ganesh, M Spence, A |
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| Affiliation: | A1 School of Mathematics, University of New South Wales, Sydney 2052, Australia A2 School of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK |
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| Abstract: | This paper is concerned with the numerical solution using orthogonalcollocation of a nonlinear integro-differential equation whichexhibits certain features arising in the modelling of catalyticcombustion in a cylindrical reactor taking account of radiation.These features imply that the available convergence theory oforthogonal collocation cannot be applied directly. Optimal convergenceresults of the orthogonal collocation approximation are provedfor our equation, and these are illustrated by numerical experiments.In addition superconvergence results for the iterated collocationsolution are obtained. |
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