The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure equations that exploited by leapfrog. We address how best integrate physics into Following Crank-Nicolson method, one approach time-center in linear solver and use Newton...

This article is devoted to the numerical study of a nonlinear Schrödinger equation in which the coefficient in front of the group velocity dispersion is multiplied by a real valued Gaussian white noise. We first perform the numerical analysis of a semi-discrete Crank-Nicolson scheme in the case when the continuous equation possesses a unique global solution. We prove that the strong order of co...

Operator splitting is a powerful concept used in many diversed elds of applied mathematics for the design of eeective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an eecient nonlinear diiusion ltering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from diierent perspectives. We start ...

We derive novel, fast, and effective preconditioned iterative methods for steady time-dependent Navier--Stokes control problems. Our approach may be applied to problems which are discretized using backward Euler or Crank--Nicolson is also a valuable candidate Stokes Crank--Nicolson. The key ingredients of the solver saddle-point type approximation linear systems, an inner iteration $(1,1)$-bloc...

The cylinder working fluid mean temperature, rate of heat fluxes to combustion chamber and temperature distribution on combustion chamber surface will be calculated in this research. By simulating thermodynamic cycle of engine, temperature distribution of combustion chamber will be calculated by the Crank-Nicolson method. An implicit finite difference method was used in this code. Special treat...

A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The based on standard Galerkin finite element method in spatial direction, fractional Crank-Nicolson method, and extrapolation methods temporal direction. novel discrete Grönwall inequality established. Thanks inequality, error estimate of a fully obtained. Several examples are p...

In this paper we develop a numerical approach to a fractional-order differential linear complementarity problem (LCP) arising in pricing European and American options under a geometric Lévy process. The (LCP) is first approximated by a penalized nonlinear fractional Black-Scholes (fBS) equation. To numerically solve this nonlinear (fBS), we use the horizontal method of lines to discretize the t...