Recent Advances in Numerical Solution of Fractional PDE

Recent Advances in Numerical Solution of Fractional PDE

Local radial basis function-based finite difference scheme

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Due to the adequacy of fractional derivatives for capturing memory effects, many systems can be well described by means of fractional differential equations (FDEs). This book studies the local radial basis function (RBF) collocation method to obtain the approximate solution of FDEs. The unknown solution will be calculated in two main stages. First, the time discretization of the governing problems is accomplished through the finite difference scheme. Second, the spatial variables are expanded by using local RBFs, where each basis function is approximated by a weighted linear summation of funct...