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Keywords
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delay partial differential equations , proportional delay, radial basis function, variable shape parameter,rate of convergencerate of convergencedelay partial differential equations , proportional delay, radial basis function, variable shape parameter,rate of convergencerate of convergence
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Abstract
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This work introduces a radial basis functions (RBFs) method to obtain numerical solutions of the nonlinear PDEs with proportional delay that have various applications in biology,
medicine, control theory, climate models and many others. Numerical methods for delay partial differential equations bring specific difficulties, which do not appear for equations without
delays. There is so little experience with numerical methods for solving delay PDEs. Several RBFs contain a free shape parameter, and choosing an optimal one plays an important role in the accuracy of the
method. In this article, we apply the Gaussian RBFs method based on symmetric variable shape parameter (SVSP) to solve a class of the delay PDEs. Sample results show that the proposed method is very accurate. Moreover, the proposed method is compared with the same method with the constant shape parameter (CSP) as well as other analytical and two other numerical methods. Finally, numerical rate of convergence of the numerical approximation will also be obtained.
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