# Tagged Questions

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### stability of FTCS scheme for parabolic equation

Can you suggest any method for stability analysis of FTCS scheme for the the following parabolic equation ? D.E: $u_{t}=a(x,t)u_{xx}+f(x,t,u)$, $0<x<1$, $0<t<T$, $T>0$ BCs: ...
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### 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.
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### Radial coordinate evaluation

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