# Questions tagged [differential-equations]

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### Two RK4 method in one program

I want to solve this integral using RK4 by coding in Fortran: $$R=∫1/a(t) dt → dR/dt=1/a(t) =f(t)$$ Initial point: t=0 (or a=0.001) and R=0 And I have to get a(t) by solving another ...
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### Numerical errors due to terms of the form $\frac{1}{r}$ (r goes to 0 at the boundary) while using finite difference method

I am trying to solve a system of differential equations using finite difference method. There are few terms of the form $\frac{A(r)}{r}$, both $A(r)$ and r go to zero at the boundary. Analytically ...
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### Governing equations vs Transport equations

This is a basic question. But I did not find any explanations for this. How are governing equations, like mass, momentum, energy conservations equations, different from 'Transport equation'?. Is a ...
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### What are the differences between these different forms of equation?

What are the differences between Conservative differential form, Non-conservative differential form, Conservative Integral form and Non-conservative integral form of differential equations? I know ...
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### Solved : Damped spring-mass system, wrong position, correct speed and acceleration

I am modulating a spring-mass system with gravitation and aero drag, with python programming. The spring is hanging vertically and attached a weight. The user then selects a length to drag it down ...
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### Fast and free server for computing

I have to calculate a huge differential equation. With my laptop, it's going to be computed for several days. Is there a free (I need just for 3 days) fast server for scientific calculations? My ...
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### Symplectic linear multistep method?

I'm doing a gravitational n-body simulator and I'm thinking of implementing linear multistep methods like Adam-Bashforth. But is there any symplectic multistep methods?
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### Online Parameter Estimation using steepest descent

I have a first order system which is described by the following differential equation: dx/dt = -a*x + b*u where u is the input <...
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### Why does the correlation function of this stochastic differential equation starts at different points?

I am working with the following differential equation: The equation is $$x=\beta +\sqrt{2D} \xi(t)$$ where $\xi(t)$ is a white noise term, with a reflecting wall boundary conditions. After solving ...
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### How to implement adaptive step size Runge-Kutta Cash-Karp?

Trying to implement an adaptive step size Runge-Kutta Cash-Karp but failing with this error: ...
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### Unexpected solutions solving an ODE using odeint

I am trying to solve a system of 8 coupled differential equations using scipy's odeint. I have already written my code and it runs fine, but the solutions I get are completely different from what I ...
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### Wrong results for $2$ stage multistep method $y_{n+2} - y_n = h\left[(1/3)f_{n+2} + (4/3)f_{n+1} + (1/3)f_n\right]$

I need to fix a code to utilise the $2$ stage multistep method : $$y_{n+2} - y_n = h\left[(1/3)f_{n+2} + (4/3)f_{n+1} + (1/3)f_n\right]$$ Since this is an implicit method, I used a Newton-Raphson ...
I would like to numerically solve the following system of coupled nonlinear differential equations:  -\frac{\hbar^2}{2m_a} \frac{\partial^2}{\partial x^2}\psi_a + V_{ext}\psi_a + \left( g_a |...