Eulerian time-stepping schemeTime-dependent domainsHeat equationCrank–Nicolson schemeA priori error analysisWe consider a time-stepping scheme of Crank–Nicolson type for the heat equation on a moving domain in
This motivates another scheme which allows for larger time steps, but with the trade off of more computational work per step. This method is known as the Crank-Nicolson scheme. The explicit method for the heat-equation involved a forward difference term for the time derivative and a centred ...
The preservation of the basic qualitative properties – besides the convergence – is a basic requirement in the numerical solution process. For solving the heat conduction equation, the finite difference/linear finite element Crank-Nicolson type full discretization process is a widely used approach. ...
Use the Crank-Nicolson Method. We need to discretize the space and time domain. x_i = i h = i \Delta x, \quad t_n = nk = n \Delta t, \quad U^n_i \approx u(x_i,t_n) \frac{U^{n+1}_i - U^{n}_i}{k} = \frac{\kappa}{2h^2}(U^n_{i-1} - 2U^n_i + ...
[nx,k]=0# compute L2 norm of the erroru_error=u[:,nt]-u_erms_error=compute_l2norm(nx,u_error)max_error=np.max(np.abs(u_error))# create output file for L2-normoutput=open("output.txt","w");output.write("Error details:\n");output.write("L-2 Norm = {0}\n".format(str(...
Thisarticlemainlyintroducesthefirstboundaryvalueproblemforthemixed problemofone-dimensionalheatconductionequations,andusingtheCrank-Nicolson schemetosolvethisproblem.Itmainlyinvolvesthederivationandproofofthis scheme,andtheanalysisforthestabilityandconvergenceofthismethod.Finally,we useMatlabtogivesomenumericalexperimentsto...
This paper proposes a numerical scheme for the Allen-Cahn equation that represents a phenomenological model for anti-phase domain coarsening in a binary mixture. In order to obtain a high order discretization in space, we adopt the barycentric interpolation collocation method. The semi-discretized ...
–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 and Phyllis Nicolson in the mid...
求解一维热传导方程Crank-Nicolson差分法
NLS with Dirac delta potential [9] and the compact difference scheme applied to the heat equation with Neumann boundary conditions [11], we propose a conservative Crank–Nicolson-type finite difference scheme with accuracy O(τ2+h2) and a compact finite difference scheme with accuracy O(τ2+h4...