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.

**[1]**R. Aris,*The Mathematical Theory of Diffusion and Reaction in Permeable Catalysis*, Vol. I, Clarendon Press, Oxford, London, 1975, pp. 101-239.**[2]**J. A. De Simone & J. A. Pennline, "A new asymptotic analysis of the*n*th order reaction-diffusion problem: Analytical and numerical studies,"*Math. Biosci.*, v. 40, 1978, pp. 303-318.**[3]**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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1981-0616365-8

Keywords:
Boundary value problem,
integral equation,
successive approximations,
convergence rate

Article copyright:
© Copyright 1981
American Mathematical Society