The present work aims to approximate the solution of linear time fractional PDE with Caputo Fabrizio derivative. For the said purpose Laplace transform with local radial basis functions is used. The Laplace transform is applied to obtain the corresponding time independent equation in Laplace space and then the local RBFs are employed for spatial discretization. The solution is then represented as a contour integral in the complex space, which is approximated by trapezoidal rule with high accuracy. The application of Laplace transform avoids the time stepping procedure which commonly encounters the time instability issues. The convergence of the method is discussed also we have derived the bounds for the stability constant of the differentiation matrix of our proposed numerical scheme. The efficiency of the method is demonstrated with the help of numerical examples. For our numerical experiments we have selected three different domains, in the first test case the square domain is selected, for the second test the circular domain is considered, while for third case the L-shape domain is selected.
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@article{CRMATH_2020__358_7_831_0,
author = {Kamran and Ali, Amjad and G\'omez-Aguilar, Jos\'e Francisco},
title = {A transform based local {RBF} method for {2D} linear {PDE} with {Caputo{\textendash}Fabrizio} derivative},
journal = {Comptes Rendus. Math\'ematique},
pages = {831--842},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {7},
year = {2020},
doi = {10.5802/crmath.98},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.98/}
}
TY - JOUR AU - Kamran AU - Ali, Amjad AU - Gómez-Aguilar, José Francisco TI - A transform based local RBF method for 2D linear PDE with Caputo–Fabrizio derivative JO - Comptes Rendus. Mathématique PY - 2020 SP - 831 EP - 842 VL - 358 IS - 7 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.98/ DO - 10.5802/crmath.98 LA - en ID - CRMATH_2020__358_7_831_0 ER -
%0 Journal Article %A Kamran %A Ali, Amjad %A Gómez-Aguilar, José Francisco %T A transform based local RBF method for 2D linear PDE with Caputo–Fabrizio derivative %J Comptes Rendus. Mathématique %D 2020 %P 831-842 %V 358 %N 7 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.98/ %R 10.5802/crmath.98 %G en %F CRMATH_2020__358_7_831_0
Kamran; Ali, Amjad; Gómez-Aguilar, José Francisco. A transform based local RBF method for 2D linear PDE with Caputo–Fabrizio derivative. Comptes Rendus. Mathématique, Tome 358 (2020) no. 7, pp. 831-842. doi : 10.5802/crmath.98. http://www.numdam.org/articles/10.5802/crmath.98/
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