In this paper, a parareal method is proposed for the parallel-in-time integration of time-fractional differential equations (TFDEs). It is a generalization of the original parareal method, proposed for classic differential equations. To match the global feature of fractional derivatives, the new method has in the correction step embraced the history part of the solution. We provide a convergenc...

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

In this paper, the multi-step differential transform method (MDTM), one of the most effective method, is implemented to compute an approximate solution of the system of nonlinear differential equations governing the problem. It has been attempted to show the reliability and performance of the MDTM in comparison with the numerical method (fourth-order Runge–Kutta) and other analytical methods su...

In this paper the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their Lp-consistency, numerical Lp-stability and Lpconvergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-squa...