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Predictor-corrector formulas based on rational interpolants
Journal article   Open access   Peer reviewed

Predictor-corrector formulas based on rational interpolants

Yudell L. Luke, Wyman Fair and Jet Wimp
Computers & mathematics with applications (1987), v 1(1), pp 3-12
1975
DOI: https://doi.org/10.1016/0898-1221(75)90003-6
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https://doi.org/10.1016/0898-1221(75)90003-6View
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Abstract

Title formulas are developed for particular use in the solution of nonlinear differential equations which in general offer no clue as to the presence of singularities on or near the path of integration. Procedure is advantageous since the approximations ascertain the existence of zeros and poles and locate these data with great accuracy. The function y = J 1( x)/ J o( x) where J n( x) is the Bessel function of the first kind satisfies a first order nonlinear differential equation of the Riccati type, and has an infinite number of zeros and poles on the positive real axis. A numerical example is provided to illustrate computation of these singular points in 0 < x < 100. Some other examples are also given.

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