Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The generalized quasilinearization method for parabolic integro-differential equations

Authors: A. S. Vatsala and Liwen Wang
Journal: Quart. Appl. Math. 59 (2001), 459-470
MSC: Primary 35K60; Secondary 35B05, 45K05
DOI: https://doi.org/10.1090/qam/1848528
MathSciNet review: MR1848528
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Abstract: In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differential equation. These comparison results are used to develop monotone sequences and to establish quadratic convergence.

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DOI: https://doi.org/10.1090/qam/1848528
Article copyright: © Copyright 2001 American Mathematical Society

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