A meshless technique based on the radial basis functions for solving systems of partial differential equations

Nemati, Mehran; Shafiee, Mahmoud; Ebrahimi, Hamideh

doi:10.22034/cmde.2021.39707.1740

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

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	A meshless technique based on the radial basis functions for solving systems of partial differential equations
Computational Methods for Differential Equations
مقاله 18، دوره 10، شماره 2، تیر 2022، صفحه 526-537 اصل مقاله (299.63 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.39707.1740
نویسندگان
Mehran Nemati؛ Mahmoud Shafiee ؛ Hamideh Ebrahimi
Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
چکیده
The radial basis functions (RBFs) methods were first developed by Kansa to approximate partial differential equations (PDEs). The RBFs method is being truly meshfree becomes quite appealing, owing to the presence of distance function, straight-forward implementation, and ease of programming in higher dimensions. Another considerable advantage is the presence of a tunable free shape parameter, contained in most of the RBFs that control the accuracy of the RBFs method. Here, the solution of the two-dimensional system of nonlinear partial differential equations is examined numerically by a Global Radial Basis Functions Collocation Method (GRBFCM). It can work on a set of random or uniform nodes with no need for element connectivity of input data. For the timedependent partial differential equations, a system of ordinary differential equations (ODEs) is derived from this scheme. Like some other numerical methods, a comparison between numerical results with analytical solutions is implemented confirming the efficiency, accuracy, and simple performance of the suggested method.
کلیدواژه‌ها
Global meshless method؛ Radial basis functions؛ Method of lines؛ Partial differential equations

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A meshless technique based on the radial basis functions for solving systems of partial differential equations