0]=-np.sin(np.pi*x[i])# store solution at t=0u_e[i]=-np.exp(-t)*np.sin(np.pi*x[i])# theory solutionbeta=alpha*dt/(dx**2)print(" beta = ",beta)a=np.zeros(nx+1)b=np.zeros(nx+1)c=np.zeros(nx+1)d=np.zeros(nx+1)half=1.0/2.0r=half*alpha...
A novel subgridding scheme using the Crank-Nicolson (CN) method to update the field components in the fine grid region is proposed in this article. Combined with the Douglas-Gunn algorithm to convert the block tri-diagonal matrix of the CN method into pure tri-diagonal form, the proposed ...
Crank-Nicolson Implicit Scheme Tridiagonal Matrix Solver via Thomas Algorithm In theprevious tutorialon Finite Difference Methods it was shown that the explicit method of numerically solving the heat equation lead to an extremely restrictive time step. This motivates another scheme which allows for larger...
In numerical analysis, the Crank –Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations.[1] It is a second-order method in time, implicit in time, and is numerically stable. The method was developed by John Crank...
最后,用数值实验验证了新方法的收敛性㊁稳健性和有效性.关键词:美式K o u 型跳扩散期权;C r a n k -N i c o l s o n 拟合有限体积法;收敛性分析中图分类号:O 241.82 文献标志码:A 文章编号:1671-5489(2022)03-0531-12 C r a n k -N i c o l s o nF i t t e dF i n i...
method so as to remarkably decrease the number of imported auxiliary variables and optimize the memory; dispersing a time domain Maxwell equation by utilizing a Crank-Nicolson time domain finite difference method so as to derive an explicit iterative equation of an electric field; and finally ...
ALGORITHMPROPAGATIONGMRESUnconditional stability of the Crank-Nicolson Finite Difference Time Domain (CN-FDTD) method permits us to use time steps over the Courant-Friedrich-Lewy (CFL) limit of conventional FDTD method. However, in this work it was realized that, when the time step is set above...
The Crank–Nicolson method is used for time discretization, and the fourth-order quasicompact technique is used for space direction. Theoretically, the derived numerical schemes can achieve second-order accuracy in time direction and fourth-order accuracy in space direction under certain constraints of...
Abstract In this article, a second-order Crank–Nicolson weighted and shifted Grünwald integral (WSGI) time-discrete scheme combined with finite element method is studied for finding the numerical solution of the multi-dimensional time-fractional wave equation. The time-fractional wave equation with ...
The primary focus now is on studying the performance in detail of the updated Crank–Nicolson algorithm because that algorithm has been very popular in the field of financial engineering [25] due to its simplicity of implementation. We also give an example of a fourth order scheme with optimal...