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...

This paper concentrates on temperature distribution in the gas turbine blade equipped by cooling holes system transient heat transfer. The present study requires specification of internal and external boundary conditions. calculations had been done using both Crank-Nicolson algorithm, explicit implicit methods, which different transfer coefficients surfaces were applied. value has a direct cruc...

In this paper we transfer the a priori error analysis for the discretization of parabolic optimal control problems on domains allowing for H regularity (i.e. either with smooth boundary or polygonal and convex) to a large class of nonsmooth domains. We show that a combination of two ingredients for the optimal convergence rates with respect to the spatial and the temporal discretization is requ...

This paper proposes a numerical method to obtain an approximation solution for the time-fractional Schrödinger Equation (TFSE) based on combination of cubic trigonometric B-spline collocation and Crank-Nicolson scheme. The fractional derivative operator is described in Caputo sense. L1−approximation used discretization. Using Von Neumann stability analysis, proposed technique shown be condition...

This paper presents the Runge–Kutta–Legendre (RKL) finite difference scheme, allowing for an additional shift in its polynomial representation. A short presentation of stability region, comparatively to Runge–Kutta–Chebyshev scheme follows. We then explore problem pricing American options with RKL under one factor Black–Scholes and two Heston stochastic volatility models, as well butterfly spre...

By incorporating the higher order concept, piece-wise linear recursive convolution (PLRC) method and Crank-Nicolson Douglas-Gunn (CNDG) algorithm, unconditionally stable complex frequency shifted nearly perfectly matched layer (CFS-NPML) is proposed to terminate left-handed material (LHM) domain. The scheme takes advantages of CFS-NPML formulation, concept PLRC CNDG algorithm in terms absorbing...

A practical computational scheme based on time-dependent density functional theory TDDFT and ultrasoft pseudopotentials USPP is developed to study electron dynamics in real time. A modified Crank-Nicolson time-stepping algorithm is adopted, under plane-wave basis. The scheme is validated by calculating the optical absorption spectra for a sodium dimer and a benzene molecule. As an application o...

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to...