# Questions tagged [ode]

Ordinary Differential Equations (ODEs) contain functions of only one independent variable, and one or more of their derivatives with respect to that variable. This tag is intended for questions on modeling phenomena with ODEs, solving ODEs, and other related aspects.

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### Estimating error at mid timesteps for Runge-Kutta methods

When a timestep $h$ is rejected using a Runge-Kutta pair, such as Dormand–Prince, the algorithm resumes from the same initial point $t$ with a smaller timestep. A different idea is to resume at an ...
1answer
173 views

### Can a second-order ODE be “inconsistent” with its boundary conditions?

I am trying to solve a set of coupled, nonlinear ODEs. The only dependent variable is a 1-dimensional spatial coordinate, let's call it $x$. For now, I've managed to approximate away some of the ...
0answers
85 views

### Solving an ODE from many starting points

I have a situation where I'm interested in solving the same ODE many times, from different initial locations. More precisely, I'm interested in solving an ODE of the form \begin{align} \frac{dx}{dt} &...
1answer
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0answers
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### Finite differenced eigenvalue prob. of inhomogeneous boundary conditions?

I am basically asking about eigenvalue problems of differential equations using some finite difference method (FDM). Usually the system is subject to some boundary conditions (BC), e.g., Dirichlet or ...
2answers
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### What does “symplectic” mean in reference to numerical integrators, and does SciPy's odeint use them?

In this comment I wrote: ...default SciPy integrator, which I'm assuming only uses symplectic methods. in which I am refering to SciPy's odeint, which uses ...
0answers
108 views

### How to account for the interface between two different phases in a discretized diffusion model?

I have tried to set up a model for the diffusion of a gas into a liquid. The two media are next to each other and the geometry is spherical because the system should simulate the diffusion out of a ...
1answer
170 views

### Implementation details for high order IMEX methods by Kennedy and Carpenter

This question is a continuation of Fourth order IMEX Runge-Kutta method, concerning the implementation. Is seems to me that the first implicit stage value involves a direct evaluation, rather than ...
1answer
125 views

### Runge-Kutta timestep in atomic units

I'm using 4th order RK to solve the schroedinger equation in atomic units. Say I want to simulate 400fs in intervals of h=10fs, then in atomic units this is h=413a.u and 400fs=16500a.u. 4RK involves ...
2answers
74 views

1answer
284 views

### Bulirsch-Stoer algorithm to solve simple chemistry. Spanning long time intervals after stationarity

Hi all and thank you in advance. I am working on a time-dependent transport-chemistry model to study the composition of planetary atmospheres. The equations are the following \frac{\partial n(z,t)}...
1answer
2k views

### 4th order runge-kutta and harmonic oscillator [closed]

I am trying to solve equations of motion for an harmonic oscillator using 4th order runge kutta method, but as a result I get almost constant velocity and position; I feel that the problem is that I ...
1answer
219 views

### Method to solve linear, first order ODE of generalized matrix matrix form

The equation and its meaning: Consider two sets $(A)_{l=0,...,m_a},$,$(B)_{l=0,...,m_b}$ of hermitian matrices and a set of positive semidefinite matrices $(C)_{l=0,...,m_c}$. Each matrix has the ...
2answers
173 views

### Learning differential equations: a textbook

I am a Computational Biology master's student and I would like to study differential equations (both ODEs and PDEs). I tried to have a look at the available textbooks but what I found is either too ...
1answer
872 views

### Speeding up ODEINT stiff example [closed]

I am trying the implement the following odeint solver example but my differential equations are different. https://github.com/headmyshoulder/odeint-v2/blob/master/examples/stiff_system.cpp The ...
1answer
44 views

### Verifying that ODE integration generates Theoretical Stationary distribution

I am trying to simulate an ODE, like $\dot{x} = \xi(x)$ that should have a stationary distribution (a la Stat Mech). Assuming that my ODE algorithm generates time samples of my system state $x$ ...
0answers
800 views

### One Dimensional Schrodinger's Equation solution using Numerov Method

I have been trying to solve Time Independent Schrodinger's equation in one dimension using Numerov Method as discussed in this excellent lecture notes I found on net. The Numerov method can solve an ...
1answer
153 views

### Parameter identification for first order ODE

I have two arrays $f(z)$ and $z$ both indexed by k and I want to solve $\frac{df}{dz}=\mu(1-f)$ to find $\mu(z)$ What would be the best numerical method to solve this equation?