Implicit-explicit time integration of nonlinear fractional differential equations, Dr. Jorge Suzuki

Описание: Title: Implicit-explicit time integration of nonlinear fractional differential equations

Speaker: Jorge Luis Suzuki, Michigan State University, [email protected]

Abstract: Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the inverse power-law kernels deteriorates the accuracy and efficiency of many existing numerical methods. We develop two efficient first- and second-order implicit-explicit (IMEX) methods for accurate time-integration of stiff/nonlinear fractional differential equations, which are based on a linear multi-step fractional Adams-Moulton method (FAMM), followed by the extrapolation of the nonlinear force terms. In order to handle the singularities nearby the initial time, we employ Lubich-like corrections to the resulting fractional operators. To develop a fast method, we rewrite the resulting IMEX methods in the language of nonlinear Toeplitz systems, where we employ a fast inversion scheme to achieve a computational complexity of N log(N), where N denotes the number of time-steps. We present the MATLAB implementation of our method, together with numerical examples for linear/nonlinear fractional Cauchy problems. Joint work with Mohsen Zayernouri.

Repo: https://github.com/suzukijo/IMEX_FDEs

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