One-dimensional parabolic problems with interfaces are solved using a method in which orthogonal spline collocation (OSC) is employed for the spatial discretization and the Crank–Nicolson method for the time-stepping. The derivation of the method is described in detail for the case in which cubic...
Note that this is an implicit method : to get the "next" value of u in time, a system of algebraic equations must be solved. If the partial differential equation is nonlinear, the discretization will also be nonlinear so that advancing in time will involve the solution of a system of ...
dimensionality of unknown mixed finite element (MFE) solution coefficient vectors in the two-grid Crank-Nicolson MFE (TGCNMFE) method for the fourth-order extended Fisher-Kolmogorov (FOEFK) equation and to build a new two-grid reduced-dimension extrapolated Crank-Nicolson MFE (TGRDECNMFE) method...
In this repository, the lid-driven cavity problem is solved using the Crank-Nicolson/Adams-Bashforth scheme for viscous and convection terms, respectively. For spatial discretization, the second-order central difference scheme is used in a uniform staggered grid. The projection method is used to so...
A sixth-order finite difference method for solving the generalized Burgers-Fisher and generalized Burgers-Huxley equations CRANK-nicolson methodThe generalized Burgers-Huxley and generalized Burgers-Fisher equations are solved by using a new sixthorder finite difference method. ... SE Liu,Y Ge,F Tian...
Based upon the approximate Crank–Nicolson (CN) finite-difference time-domain method implementation, the unconditionally stable algorithm is proposed to investigate the wave propagation and transmission through extremely thin graphene layers. More precis
Crank–Nicolsonmethod Crank–Nicolson method From Wikipedia, the free encyclopedia
A comparison is made between the Arnoldi reduction method and the Crank–Nicolson method for the integration in time of the advection–diffusion equation. This equation is first discretized in space by the classic finite element (FE) approach, leading to an unsymmetric first-order differential ...
MethodALTERNATINGDirectionIMPLICIT(ADI)To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apace and time solved at each time level. The ...
Finally, numerical examples are presented to verify the efficiency of our method.doi:10.1186/s13661-017-0748-2Pu ZhangHai PuSpringer International PublishingBoundary Value ProblemsZhang, P., Pu, H.: The error analysis of Crank-Nicolson-type difference scheme for fractional subdiffusion equation with...