# 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.

330 questions
Filter by
Sorted by
Tagged with
119 views

### ODE System doesn't work when step size (h) is bigger than 1

I am a beginner to Python. Currently I'm writing a code for developing a simple solver for non-linear ODE systems with initial value. The equations of the system are The function of myu is evaluated ...
466 views

### Set of linear ordinary differential equations with a mass matrix

What methods are known for efficiently solving a large set of linear homogeneous ordinary differential equations of the following form? \begin{equation} \mathbf{B} \frac{d\mathbf{y}}{dt} = \mathbf{A} \...
87 views

### Fast table interpolation on regular time data for ODE

I am using scipy.integrate.odeint to simulate the reaction of a system with known input signals via integration. The simplified code below illustrates what I'm ...
794 views

### Using RK2 Method to solve the simple harmonic oscillator of a horizontal mass on a spring (1D)

Being new to numerical analysis techniques, in particular RK2, I decided the best way to jump in is by using python to solve the well known mass-spring oscillator using RK2 techniques. My problem is ...
93 views

### Stability of dark solitons in a harmonic trap

This question is based upon a research article which I am trying to reproduce. One of the main result of this paper is the condition on transverse confinement of the Bose-Einstein Condensate(BEC) to ...
112 views

### VTK: Missing Streamlines due to error in Runge-Kutta method?

We are using Kitware VTK to visualize our models. When we display streamlines, it sometimes happens that a single streamline is left out. This can be especially seen when duplicating a model several ...
435 views

### How to implement an integral condition when solving a BVP in MatLab

I am trying to solve a coupled system of ODE's using MATLAB's bvp4c function. I want to impose the condition that $$\int_{0}^{\pi} y_{1}(t) y_{1}(t) dt = 1,$$ where ...
181 views

### Trouble getting steady-state solution by solving system of nonlinear algebraic equations in MATLAB

Background I have a stiff system of 6 ODEs, represented in MATLAB as follows: ...
314 views

84 views

68 views

### Convert scipy integration with one step to matlab integration

Scipy integration allows us to do ode integration one adaptive timestep at a time and do something to it. However, matlab ode needs us to specify a timespan , and determine the adaptive timestep ...
310 views

### ODE45: doubts about the result. Correct or not?

I have to solve $$\left\{\begin{matrix} x\ddot{x}+\frac{3}{2}\dot{x}^2=\frac{1}{\rho}\left (P_v-a_1t^2-a_2t-P_0 \right )\\ x(0)=5\cdot10^{-6}\\ \dot{x}(0)=0 \end{matrix}\right.$$ I do not know if ...
6k views

### Why are higher-order Runge–Kutta methods not used more often?

I was just curious as to why high-order (i.e. greater than 4) Runge–Kutta methods are almost never discussed/employed (at least to my knowledge). I understand it requires greater computational time ...
271 views

### Comparison between CashKarp Method and Dormand Prince Method - Runge Kutta Method

Can Cash Karp Method be used for integrating a nonsmooth solution ?. Because Dormand Prince method gives an error while integrating nonsmooth solution How can nonsmooth function can be integrated? I ...
440 views

### Scaling step size in adaptive runge-kutta method

I'm developing my own generic Runge-Kutta solver, and I'm currently implementing the adaptive step-size routine. I say generic because I want to be able to test different RK implementations by only ...
237 views

### Matlab: ode45 loop

I have to solve this equation $$\ddot{x}x = -\frac{3}{2}\dot{x}^2 + \frac{\dot{x}}{h} + \sin(t)$$ where $h$ is defined by $$h = \left(\frac{\dot{x}}{h}\right)^{1/3} + \frac{\dot{x}}{h}$$ My idea ...
293 views

### Which ODE solver in Matlab allows me to advance in just one timestep only

[t,y] = odeXX(odefun,tspan,y0) I have a solver odeXX, and the tspan = [0 0.0001]. It seems that for any ode solver in MATLAB, they integrate by breaking ...
247 views

### Runge Kutta solution blows up for a first order ODE with very large coefficients

I am solving a first-order ODE: $\frac{\partial \rho }{\partial t} = -a \rho^2 + b |A(t)|^2 \rho +c|A(t)|^{2m}$ This is the evolution of the plasma density in the presence of a laser pulse (complex ...
119 views

### Numerically solving differential equations, the domain is very long, [0, +10^6), so the calculating time is very long

Is there any method to deal with this problem? I am using Mathematica to solve the differential equations, but the calculating time is so long because of the large domain $x\in[0,10^{6})$. In fact I ...
84 views

### The Schrodinger equation for time-dependent Hamiltonian after one timestep, taking exponential or use ode solver?

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ Assuming I knew $\psi(t)$, I want to know $\psi(t+\Delta t)$. Should I take exponential ...
122 views

### Will the numerical solving of the differential equation be wrong if I take the step too small? [closed]

If I take the step too large I will get error, while if I take the step too small I also get an error. In my case, instead of seeing the function decreasing, i have it increasing if I take the step ...
335 views

### Implementing odespy for system of PDEs

After trying to use RK4 to solve the below system of equations, it appears the output had large and fast oscillations even with an adaptive time step I incorporated using the Cash-Karp method. I am ...
639 views

### Why does LSODA fail to integrate the logistic function?

I'm comparing some of the different ODE integrators in scipy.integrate.ode on solving the logistic function: $$x(t) = \frac{1}{1+e^{-rt}}$$ $$\dot{x} = rx(1-x)$$ ...
388 views

### Use of scipy sparse in ode solver

I am trying to solve a differential equation system $$x´=Ax\quad \text{with } x(0) = f(x)$$ in Python, where $A$ indeed is a complex sparse matrix. For now i have been solving the system using the ...
299 views

### Object falling with air resistance using Runge-Kutta

I am not very familiar with differential equations, nor physics in general. I am trying to program an object falling with air resistance with the use of a numerical algorithm called Runge-Kutta. The ...
4k views

### Which Runge-Kutta method is more accurate: Dormand-Prince or Cash-Karp?

I simply want to know whether the Dormand-Prince Numerical Method or the Cash-Karp Numerical Method is more accurate.
217 views

### Solving a differential equation using numerical methods and matlab

(a) Consider the following differential Equation $$Y'(t)=\frac{1}{1+t^{2}}-2[Y(t)]^2$$ $$Y(0)=0$$ The exact solution is $$Y(t)=\frac{t}{1+t^2}$$ Using the Euler method to solve the following ...
523 views

### How to properly implement Backwards Euler on a system of bodies

I have a system of two bodies, $b^i$ and $b^j$, each in position $\vec{p}^i = (x^i, y^i)$ and $\vec{p}^j = (x^j, y^j)$. The two are connected via spring and I'd like to know, given their states at ...
69 views

### Solving ODEs of Switched Systems using MATLAB ODE suite

I have the following code to execute: $X$ = [0;0;0;0]; $sw$ = 0; ...
79 views

### Solve ODE with initial values using Laplace transform

I am trying to solve ordinary differential equations with initial conditions using Laplace transform. A simple test setup includes an exponential discharge of RC circuit and an integrator from ...
111 views

### Solving ODE with multiple equilibriums

Consider an ODE of the form: $$u'(t)=-\frac{1}{\varepsilon}u(u-\frac{1}{2})(u-1)$$ with the initial value $$u(0)=u_0.$$ Here $\varepsilon>0$ is a constant. It is easy to verify that $u\equiv0$ ...