A meshfree method based on the radial basis functions for solution of two-dimensional fractional evolution equation

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• 作者：Hadi Roohani Ghehsareh^a ; ^{hadiroohani61@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Sayna Heydari Bateni^b ; Ali Zaghian^a
• 关键词：Fractional evolution equation ; Meshfree method ; Radial basis functions
• 刊名：Engineering Analysis with Boundary Elements
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：61
• 期：Complete
• 页码：52-60
• 全文大小：1071 K

文摘

In the current work, numerical solution of a two-dimensional fractional evolution equation has been investigated by using two different aspects of strong form meshless methods. In the first method a time discretization approach and a numerical technique based on the convolution sum are employed to approximate the appearing time derivative and fractional integral operator, respectively. It has been proven analytically that the time discretization scheme is unconditionally stable. Then a meshfree collocation method based on the radial basis functions is used for solving resulting time-independent discretization problem. As the second approach, a fully Kansa壮s meshfree method based on the Gaussian radial basis function is formulated and well-used directly for solving the governing problem. In this technique an explicit formula to approximate the fractional integral operator is computed. The given techniques are used to solve two examples of problem. The computed approximate solutions are reported through the tables and figures, also these results are compared together and with the other available results. The presented results demonstrate the validity, efficiency and accuracy of the formulated techniques.