0
votes
0answers
49 views

How can solve this differential equation (third equation )?

How can I solve this differential equation? $$ \frac{dy}{dx}=\sqrt{\frac{A}{y}+\frac{B}{y^2}+\frac{C}{y^4}+\frac{D}{y^5}+\frac{1}{(\frac{1}{y}+\frac{3}{y^2})^2}} $$ where $A,B,C,D$ are constants.
2
votes
1answer
88 views

Radial coordinate evaluation

Details of the question can be found in the article equation(55,56) A radial coordinate $R$ defined by \begin{equation} r=\frac{2R}{\kappa(1-R^2)} \,, \end{equation} where $\kappa$ is a constantand ...
1
vote
1answer
30 views

Conjuagate Gradient on Periodic BCs

I'm currently writing a CG solver. It works perfectly fine for Dirichlet boundary conditions, however, I also want it to work with periodic BCs. The problem I'm solving is a 3D Poisson equation. I ...
0
votes
1answer
211 views

butcher tableau for given algorithm

Given $y'(t) = f(t,y(t))$ and the following algorithm: $$y_{n+\frac{1}{2}} = y_n + \frac{h}{2}f(t_n,y_n)$$ $$y_{n+1} = y_n + hf(t_n+\frac{h}{2},y_{n+\frac{1}{2}})$$ We should show that this can be ...
2
votes
2answers
216 views

1st-order linear ODE with tridiagonal matrix. Efficient solutions?

I have a 1st-rder linear ODE system where the system is characterized by $A$. Given an initial state $x_0$, I want the state at some later time $t$, efficiently. $A$ happens to be a symmetric ...
3
votes
2answers
265 views

Generating unitary matrices numerically - “close” to the identity element

EDIT: broke this into two parts - for these were two different questions. For numerically obtaining the stabilities of a matricial equation, i need to generate an ensemble of matrices that are ...