A general mesh independence principle for Newton's method applied to second order boundary value problems |
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| Authors: | Dr. E. L. Allgower F. St. McCormick D. V. Pryor |
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| Affiliation: | 1. Department of Mathematics, Colorado State University, 80523, Fort Collins, CO, U.S.A.
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| Abstract: | Recent work has established that for certain classes of nonlinear boundary value problems, the number of Newton iterations applied to the related standard discrete problem for a given tolerance is independent of the mesh size when the mesh is sufficiently fine. This paper develops an extension of the mesh independence principle by relaxing the assumption on the differential equation, its boundary conditions, and the related difference approximation. |
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