MMN-3125
On the local transformed based method for partial integro-differential equations of fractional order
Marjan Uddin; Muhammad Taufiq;Abstract
In the present work, a localized Laplace transform based numerical
scheme is constructed for fractional partial integro-differential equations
with weakly singular kernels. By application of the Laplace transform the
time variable is eliminated and the spatial derivatives are approximated by
RBFs which transformed the problem into a linear system of equations. The
resultant system lead to differentiation matrices which are sparse contrary
to large global collocation matrices. The inverse Laplace transform is then
computed numerically using contour integration to recover the solution. The
efficiency and accuracy of the method is demonstrated by several numerical
experiments. The results obtained by the present method are compared with
analytical solutions and other numerical methods.
Vol. 21 (2020), No. 1, pp. 435-449