Abstract
In this paper, the question of whether it is possible to develop monotone sequences that converge to the solution quadratically, when the function involved in the initial-value problem admits a decomposition into a difference of two convex functions, is answered positively. This extends the method of quasilinearization to a larger class.
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References
Bellman, R.,Methods of Nonlinear Analysis, Vol. 2 Academic Press, New York, New York, 1973.
Bellman, R., andKalaba, R.,Quasilinearization and Nonlinear Boundary-Value Problems, American Elsevier, New York, New York, 1965.
Ladde, G. S., Lakshmikantham, V., andVatsala, A. S.,Monotone Iterative Techniques for Nonlinear Differnntial Equations, Pitman, Boston, Massachusetts, 1985.
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Communicated by R. E. Kalaba
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Lakshmikantham, V. An extension of the method of quasilinearization. J Optim Theory Appl 82, 315–321 (1994). https://doi.org/10.1007/BF02191856
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DOI: https://doi.org/10.1007/BF02191856