John J. Garwood, Samuel N. Jator
Abstract:
Numerical methods based on polynomial approximation perform poorly when
applied to singular initial value problems (IVPs). Hence, we are
motivated to derive and implement numerical methods involving non-polynomial
basis functions such as logarithmic and rational functions. Specifically, by
imbedding a constant parameter into the logarithmic function, we are able to
improve any discontinuity issues with the natural logarithm approximant.
An efficient method is developed using the Taylor Series expansion to optimize
the imbedded parameter. Numerical experiments performed show that this method
is more accurate than the improved Euler's method. This method is implemented
as a predictor-corrector method.
Published March 21, 2016.
Math Subject Classifications: 65L05, 65L06.
Key Words: Singular initial value problem; rate of convergence;
rational logarithmic basis function.
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John J. Garwood Department of Mathematics and Statistics Austin Peay State University Clarksville, TN 37044, USA email: jgarwood1@my.apsu.edu | |
Samuel N. Jator Department of Mathematics and Statistics Austin Peay State University Clarksville, TN 37044, USA email: jators@apsu.edu |
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