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Title
Numerical Solution of nonlinear PDEs with proportional delay using RBF method based on variable shape parameter strategy‎
Type of Research Presentation
Keywords
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
Abstract
‎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.
Researchers Mojtaba Ranjbar (First Researcher)، Vahid Roomi (Second Researcher)