Abstract
The objective of this paper is the development of a mesh refinement technique for applying Newton’s method to the solution of nonlinear two-point boundary value problems. The process represents a significant improvement on an earlier approach both in its general applicability and in its numerical performance. This is demonstrated by several reported numerical examples.
This work was supported by the National Science Foundation under grant number MCS76-09215.
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References
E. L. Allgower and S. F. McCormick, A phenomenon concerning Newton’s method for boundary value problems and its application to mesh refinement, Numer. Math., to appear.
E. L. Allgower, S. F. McCormick, and D. V. Pryor, A general mesh independence principle for Newton’s method applied to second order boundary value problems, submitted for publication.
E. L. Allgower, On a discretization of y″ + λyk=0, Topics in Numerical Analysis II, ed. J. J. H. Miller, New York, Academic Press, (1975) 1–15.
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McCormick, S.F. (1978). A revised mesh refinement strategy for newton’s method applied to nonlinear two-point boundary value problems. In: Ansorge, R., Törnig, W. (eds) Numerical Treatment of Differential Equations in Applications. Lecture Notes in Mathematics, vol 679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067863
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DOI: https://doi.org/10.1007/BFb0067863
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