Questions tagged [crank-nicolson]
For questions about the Crank-Nicolson method, an approach for discretizing and solving partial differential equations.
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Crank–Nicolson method for nonlinear differential equation
I want to solve the following differential equation from a paper with the boundary condition:
The paper used the Crank–Nicolson method for solving it. I think I understand the method after googling ...
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implicit method (crank-Nicolson) I not understand the procedure [closed]
I'm trying to understand the passage through this equation can be written for easily solved with the fortran alghorithm in particular i don't understood the meaning of L_x and L_xx ... what (-1,0,1) ...
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Crank-Nicolson scheme in space for advection equation
Consider the equation
$$\frac{\partial}{\partial t}v(t,x)=\frac{\partial}{\partial x}v(t,x)$$,
for $t,x\in\mathbb{R}$.
I'd like to solve this equation forward in space and backward in time, ...
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Crank-Nicolson algorithm for coupled PDEs
Assumed I have the following two coupled equations
$$\begin{split}
\partial_tA&=a_0AB\\
\partial_tB&=b_0AB
\end{split}
$$
but I am not sure how to calculate them. One approach is a crank-...
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Why can I not solve the negative advection equation (backwards in time)?
Suppose we have the negative, inhomogeneous advection equation:
$$\left(\frac{\partial}{\partial x}-\frac{1}{c}\frac{\partial}{\partial t}\right)v(t,x)=u(t,x)\qquad(t\in\mathbb{R}_{+},x\in\mathbb{R})$$...
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Crank-Nicolson method for inhomogeneous advection equation
Suppose we have the inhomogeneous advection equation
$$\left(\frac{\partial}{\partial x}+\frac{1}{c}\frac{\partial}{\partial t}\right)u(t,x)=v(t,x)$$
for $u,v:\mathbb{R}\times\mathbb{R}\to\mathbb{R}$ (...
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Solving an equation in space and time using the Crank-Nicolson approach
Assume I have the following equation (light propagating in $z$-direction through the matter):
$$id_zu+d^2_ru=0$$
with $u(z, r)$ being a complex wave. The time scale in this equation is
$$t\equiv t_\...
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What is the origin of the spurious oscillations in the Crank-Nicolson scheme?
I was reading about the Crank-Nicolson method, and it is often said that it can produce "spurious oscillations" or that this method is prone to "ringing", especially for large time step and stiff ...
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How can I numericaly solve a convection-diffusion equation with a large diffusion term?
I want to numerically solve the advection-diffusion equation:
\begin{equation}
u_t(x,t) + cu_x(x,t) = v u_{xx}(x,t)
\end{equation}
for $x \in [0,1]$ and $t \geq 0$ subject to the boundary conditions ...
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Numerical solution of non-linear heat-diffusion PDE using the Crank-Nicolson Method
I am trying to solve numerically the following 1D EBM:
$C\frac{\partial T[x,t] }{\partial t} - \frac{\partial }{\partial x}\left ( D(1-x^2)\frac{\partial T[x,t] }{\partial x} \right ) + I[T] = S[x,t](...
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How to handle boundary conditions in Crank-Nicolson solution of IVP-BVP?
I'm trying to solve the PDE for $c(r,t)$
$$c_t=(1/r)(rJ)_r$$
using Crank-Nicolson, and I'm having difficulty with the boundary conditions. $J$ is the flux, the initial condition is $c(0,r)=c_{init}$, ...
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Useful Quantity for Heat Equation? [duplicate]
I'm interested in testing some algorithms on the heat equation, and I'd like to assess their accuracy. When evolving a Hamiltonian system, one has the energy to check the validity/correctness of the ...
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Numerical solution of burgers equation with finite volume method and crank-nicolson
I'm having difficulty with numerically solving the inviscid burgers equation.Godunov's scheme is used in most of what I've found in literature . Now my question is if using a crank nicolson shceme is ...
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Is this system of diffusion equations well-posed?
I’m using a standard Crank-Nicholson algorithm to solve this system of two coupled diffusion equations:
$$\dot{u} - \dot{v} = \frac{\partial}{\partial x} \left( \alpha(x) \frac{\partial u}{\partial x}...
user20536
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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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