Tenth MSU Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 23 (2016), pp. 17.
Using rational logarithmic basis functions to solve
singular differential equations
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 nonpolynomial
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 predictorcorrector 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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