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Tagged with crank-nicolson algorithms
2
questions
3
votes
1
answer
136
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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 ...
- 303
0
votes
1
answer
587
views
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_\...
- 563