ON THE LOCAL TRANSFORMED BASED METHOD FOR PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

摘要

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 RBF 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.