The weighting subspaces of the Tau Method and orthogonal collocation |
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Authors: | MK El-Daou EL Ortiz |
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Institution: | a Applied Sciences Department, College of Technological Studies, POB 64287 Shuwaikh/B, 70453 Kuwait b Department of Mathematics, Imperial College, London, SW7 2BZ, UK |
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Abstract: | In this paper we characterise the weighting subspaces associated with two approximation techniques for solving ordinary differential equations: the Tau Method E.L. Ortiz, The Tau Method, SIAM J. Numer. Anal. 6 (1969) 480-92] and the orthogonal collocation method. We show that approximations constructed by means of these two methods are always expressible in terms of a prescribed orthogonal polynomials basis, by projection on a suitably chosen finite dimensional weighting subspace. We show, in particular, that collocation is a special Tau Method with a twisted basis. |
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Keywords: | Orthogonal polynomials Collocation Tau Method Projection methods |
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