The Convergence of Operator Approximations at Turning Points |
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Authors: | MOORE, G. SPENCE, A. |
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Affiliation: | School of Mathematics, University of Bath Claverton Down, Bath BA2 7AY |
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Abstract: | Present address: Department of Mathematics, University of Reading, Reading RG6 2AX. We consider the convergence of solution curves of approximationsto parameter-dependent operator equations of the form G(, x)= 0. Provided Gx(, x) remains non-singular this problem is cateredfor by a simple extension to standard theory. In this paper,however, attention is concentrated on solution curves throughcertain singular points (0, x0), and the main result is thatconvergence depends on consistency and stability results forthe linear eigenvalue problem Gx(0, x0)0 = 0. |
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