Questions tagged [crank-nicolson]
For questions about the Crank-Nicolson method, an approach for discretizing and solving partial differential equations.
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Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation
I don't understand the different behaviour of the advection-diffusion equation when I apply different boundary conditions. My motivation is the simulation of a real physical quantity (particle density)...
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Is the maximum/minimum principle of the heat equation maintained by the Crank-Nicolson discretization?
I'm using the Crank-Nicolson finite difference scheme to solve a 1D heat equation. I'm wondering if the maximum/minimum principle of the heat equation (i.e. that the maximum/minimum occurs at the ...
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How to discretize the advection equation using the Crank-Nicolson method?
The advection equation needs to be discretized in order to be used for the Crank-Nicolson method. Can someone show me how to do that?
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What is the origin of the spurious oscillations in the Crank-Nicolson scheme?
I was reading about the Crank-Nicolson method, and it is often said that it can produce "spurious oscillations" or that this method is prone to "ringing", especially for large time step and stiff ...
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2
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Is this system of diffusion equations well-posed?
I’m using a standard Crank-Nicholson algorithm to solve this system of two coupled diffusion equations:
$$\dot{u} - \dot{v} = \frac{\partial}{\partial x} \left( \alpha(x) \frac{\partial u}{\partial x}...
user20536
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2
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Is the diffusion equation with Neumann and Dirichlet BCs well-posed?
I am considering the following diffusion equation:
$$\frac{\partial f}{\partial t} = \frac{\partial}{\partial x}[D(x,t)\frac{\partial f}{\partial x}]$$
over a grid ...
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Why is Crank-Nicolson considered implicit in time?
From Wikipedia:
Explicit methods calculate the state of a system at a later time from
the state of the system at the current time, while implicit methods
find a solution by solving an equation ...
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Finite Differencing schemes for Convection-Diffusion equation
I'm using the Convection(/advection)-Diffusion(-Reaction) equation to calculate the temperature over time in different hydraulic parts like a pipe or a heat exchanger.
The flow/convection is always 1D,...
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0
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Stability of Crank-Nicholson for advection diffusion equation for spatial discretization other than finite differences second-order centered
Crank Nicholson is a time discretization method (see 4th equation here). From what I see around, you can use different space discretization, such as Finite elements. But for the linear advection-...
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Order of convergence of Scrodinger eq. with CN scheme
I'm trying to solve numerically the 1-dim time dependent Schrodinger equation using the Crank Nicolson scheme and the Thomas algorithm to solve the tridiagonal matrix.
The physical system consists of ...
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1
answer
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My algorithm for the heat equation is unstable
I have implemented the 2D heat equation with what I thought was the Crank-Nicolson algorithm in the following way:
...
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1
answer
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Method to linearize highly nonlinear partial differential equation
I have a set of coupled pdes which I want to solve using finite-difference, of which one is nonlinear. The three linear pdes for quantities $T_f$, $T_s$ and $c$ are convection-diffusion-reaction-like ...
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How to handle boundary conditions in Crank-Nicolson solution of IVP-BVP?
I'm trying to solve the PDE for $c(r,t)$
$$c_t=(1/r)(rJ)_r$$
using Crank-Nicolson, and I'm having difficulty with the boundary conditions. $J$ is the flux, the initial condition is $c(0,r)=c_{init}$, ...
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Derivation of a parabolic PDE using Alternating Direction Implicit method
I have a very simple question concerning Alternating Direction Implicit (ADI) Scheme.
If I have an equation of the form:
\begin{equation*}
\frac{df(x,y,t)}{dt} = \nabla^2 f(x,y,t) + f(x,y,t)
\end{...
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Maintain unitary time evolution for a nonlinear ODE
I want to solve a nonlinear ODE of matrix $A(t)$
$$\mathrm{i}\dot A = A(t)M(t),\:\mathrm{with}\: M(t)=A^\dagger(t)H(t)A(t)$$ where $H(t)$ and hence $M(t)$ are Hermitian. Therefore, I presume the time ...
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