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

Abstract

In this article, we use the collocation method based on the radial basis functions with sym- metric variable shape parameter (SVSP) to obtain numerical solutions of neutral-type functional- differential equations with proportional delays. We used Gaussian radial basis functions with SVSP. Using non uniform collocation points, we achieved a system and solving this system yielded the prob- lem solutions. 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). Finally, numerical rate of convergence analysis of the numerical approximation was also obtained. It is observed that by comparing be- tween the obtained ROC values of error norms by the SVSP and CSP method, SVSP results were considered acceptable.