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Abstract
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In this article, we use the collocation method based on the radial basis functions with symmetric variable shape
parameter (SVSP) to obtain numerical solutions of neutral-type functional-differential equations with proportional
delays. In this method, we control the absolute errors and the condition number of the system matrix through
the program prepared with Maple 18.0 by increasing the number of collocation points that have a direct effect
on the de ned shape parameter. Also, we present the tables of the rate of the convergence (ROC) to investigate
and show the convergence rate of this method compared to the RBF method with constant shape parameter.
Several examples are given to illustrate the efficiency and accuracy of the introduced method in comparison with
the same method with the constant shape parameter (CSP) as well as other analytical and numerical methods.
Comparison of the obtained numerical results shows the considerable superiority of the collocation method based
on RBFs with SVSP in accuracy and convergence over the collocation method based on the RBFs with CSP and
other analytical and numerical methods for delay differential equations (DDEs).
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