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Mathematics of Computation

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Improving convergence rate in the method of successive approximations

Author: James A. Pennline
Journal: Math. Comp. 37 (1981), 127-134
MSC: Primary 65R20; Secondary 34B15, 65L10
MathSciNet review: 616365
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Abstract: An application of the method of successive approximations for obtaining the solution of a nonlinear integral equation arising from a two-point boundary value problem is illustrated. In particular, we show sufficient conditions under which the convergence rate of the sequence can be improved.

References [Enhancements On Off] (What's this?)

    R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysis, Vol. I, Clarendon Press, Oxford, London, 1975, pp. 101-239. J. A. De Simone & J. A. Pennline, "A new asymptotic analysis of the nth order reaction-diffusion problem: Analytical and numerical studies," Math. Biosci., v. 40, 1978, pp. 303-318.
  • Herbert B. Keller, Numerical methods for two-point boundary-value problems, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0230476

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Keywords: Boundary value problem, integral equation, successive approximations, convergence rate
Article copyright: © Copyright 1981 American Mathematical Society