Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations

Document Type : Research Paper

Authors

1 Department of Mathematics, Guilan Science and Research Branch, Islamic Azad University, Rasht, Iran.

2 Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

3 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

4 Faculty of Financial Sciences, Kharazmi University, Tehran, Iran.

Abstract

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 defined 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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