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I am trapped here for a long time. I wrote a toy Matlab FEM code. I want to run the follow simulation.MeshSuppose we have a cube, and we divide it...
Asked on 08/22/2021
2 answerI have a question about the Markov Chain Hamiltonian Monte Carlo (MCHMC).Hamiltonian Monte Carlo is known as Hybrid Monte Carlo too. I'll describe the steps of the algorithm.We have...
Asked on 08/22/2021 by Eleuname
1 answerI have a large number of parallel processes and a large integer $n$, and want to randomly partition the integers $[0,n)$ among the processes with only $O(1)$...
Asked on 08/22/2021 by Geoffrey Irving
1 answerI would like to use Runge-Kutta 8th order method (89) in a celestial mechanics / astrodynamics application, written in C++, using a Windows machine. Therefore I wonder if anyone knows...
Asked on 08/22/2021
4 answerSome older books I've seen say that the minimum number of stages of an explicit Runge-Kutta method of a specified order is unknown for orders $geq 9$. Is this still...
Asked on 08/22/2021
2 answerIn FEM classes, it's usually taken for granted that the stiffness matrix is positive definite, but I just can't understand why. Could anyone give some explanation? For instance, we can...
Asked on 08/22/2021
2 answerLet $d_1=1,d_2=2,a_{11}=frac{5}{13},a_{12}=frac{22}3,a_{21}=-2,a_{22}=frac{6}7,tau=frac{5}7$, $psi(t,x)=cos^42x,phi(t,x)=frac{3}{13}x^4sin^2 3x$, $Omega=[0,200]$ How to solve: $$left{begin{array}{lc} dfrac{partial u(t,x)}{partial t}=d_1triangle u(t,x)+u(t,x)left(r_1-a_{11}u(t-tau,x)-a_{12}v(t,x)right),& t>0,xinOmegadfrac{partial v(t,x)}{partial t}=d_2triangle v(t,x)+v(t,x)left(-r_2+a_{21}u(t,x)-a_{22}v(t,x)right),& t>0,xinOmegadfrac{partial u}{partial n}=dfrac{partial v}{partial n}=0,quad tge0,xinpartialOmega quad(text{Neumann conditions})u(t,x)=phi(t,x)ge...
Asked on 08/22/2021 by LCFactorization
1 answerGiven a set of ODE's $ dot{z} = f(z) $ (or discrete time $ z_{t+1} = f(z_t) $), is there a way to numerically find constants of motion? For $...
Asked on 08/22/2021
3 answerI am looking for numerical packages (ideally Python) to solve second kind Volterra integral equations, such as $$u(t)=g(t)+int_0^tK(t,s)u(s) ds$$ or Volterra-Fredholm integral equations $$u(x,t)=g(t,x)+cint_0^tint_Omega K(t,s,x,xi)u(s,xi) dxi ds$$ Are there any...
Asked on 08/22/2021
1 answerI have these three differential equations in which I need to solve numerically: $$frac{dn_0}{dt}= -n_0(t)W_{01}(t) + n_1(t)K_{10}$$ $$frac{dn_1}{dt}= -n_1(t)W_{12}(t) - n_1(t)K_{10} + n_2(t)K_{21} + n_0(t)W_{01}(t)...
Asked on 08/22/2021 by M. Douglas
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