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...
F.: A semi-Lagrangian Crank- Nicolson algorithm for the numerical solution of advection- diffusion problems, Geochem. Geophys. Geosys., 7, Q04014, doi:10.1029/2005GC001073, 2006.Marc Spiegelman and Richard Katz. A semi-lagrangian crank- nicolson algorithm for the numerical solution of ...
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...
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...
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 ...
modes.Weillustratetwoapplicationsofthemethod:uncouplinggroundwater–surface waterflowsandStokesflowplusaCoriolisterm. ©2014ElsevierB.V.Allrightsreserved. 1.Introduction Theimplicit–explicit(IMEX)combinationofCrank–NicolsonandLeapfrog(CNLF)iswidelyusedinatmosphere,ocean andclimatecodes,seee.g.,[1–4],and...
Unconditionally stable auxiliary differential equation Crank-Nicolson-approximate-decoupling FDTD algorithm for 2-D anisotropic magnetized plasma 针对二维各向异性磁等离子体提出一种有效的无条件稳定算法,新算法结合了辅助微分方程(ADE)方法与Crank-Nicolson approximate-decoupling...