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.

learn more… | top users | synonyms

0
votes
0answers
8 views

Dynamically ending ODE integration in SciPy

I have a light ray moving through space-time, i.e. a curve in R⁴, parametrized by some variable λ. The exact trajectory, i.e. the coordinate functions $x^μ(λ)$ of the curve are given by some ODE ...
3
votes
0answers
38 views

Is it normal to expect the error of simulation of a damped harmonic oscillator to decrease as the damping factor decreases?

I am simulating a damped harmonic oscillator using the RK4 method of numerical integration. I am comparing the simulated results with the analytical ones (for the free evolution case) and obtaining ...
1
vote
1answer
55 views

Switch between 2 equations to be given to ODE using events

I am trying to simulate a system with bilinear stiffness described by the following equations: $25\ddot{x}+15\dot{x}+330000x = p(t)$ if $x < 0.00072$ $25\ddot{x}+15\dot{x}+930000x = p(t)$ if $x ...
1
vote
0answers
57 views

How to solve an ode with stochastic time-dependent input

I am trying to repeat an example I found in a paper. I have to solve this ODE: $25 \ddot{x} + 15 \dot{x} + 330000 x = p(t)$ where $p(t)$ is a white noise sequence band-limited into the 10-25 Hz ...
2
votes
0answers
55 views

How to tell if symplectic integrator is more suitable for my problem, and what are downsides?

This question follows another one that I have already asked. My intention was to use a classical Runge-Kutta 45 method to solve ODEs of my system. However, I have seen recommendations for using ...
1
vote
1answer
79 views

How can I call the Boost C++ odeint Runge-Kutta integrator for a system of ODEs?

I would like to use Boost C++ odeint Runge-Kutta integrator on a system that looks like this : $$\ddot x = - \frac A{||x||^3} * x $$ $ x $ is a vector in 3D space, so basicaly $ x(i, j, k) $ $ ...
1
vote
1answer
67 views

Nonlinear ODE to solve Duffing's equation

I am trying to solve the Duffing's equation in MATLAB. $ m\ddot{y}+c\dot{y}+ky+k_{3}y^{3} = f(t) $ where $ f(t) = A \sin{\omega t}$ To do that I wrote a function to be given to the ode45. ...
-2
votes
1answer
45 views

Solving electron density function for Hydrogen and drawing in 3D

I recently stumbled upon interesting site that has interactive 3D representation of radial electron distribution (atomic orbital). here is the url: ...
0
votes
0answers
67 views

2D cross section from 3D surface

I am trying to apply the "restoring force surface" method to a dynamic linear system. The idea behind this method is that, knowing acceleration, displacement, velocity and input force it is possible ...
5
votes
2answers
115 views

How does the L-stability or A-stability of a scheme relate to its ability to preserve a quadratic invariant?

I am working with the simple example of an oscillator: $$(1) \; \; \ddot{u} + u = 0, \; \; u(0) = u_0$$ I know that Forward Euler does not preserve an invariant of the above system: $$(2) \; \; ...
2
votes
0answers
50 views

Solvers for stiff initial value ODEs with sparse Jacobian

What ODE solvers are optimized for solving stiff systems with sparse Jacobian? Such systems appear, for instance, when a parabolic PDE is discretized in space using typical finite difference or finite ...
-1
votes
1answer
46 views

Libraries with the method of lines for parabolic PDEs [closed]

Could you please advise some programs or libraries for solving parabolic PDEs (or its systems) in 1D, 2D and 3D, for example, with the method of lines? The system of parabolic PDEs can be nonlinear in ...
1
vote
1answer
41 views

Matlab equivalent of scipy's 'vode' and 'zvode' ode routines

In python I have used the ode method from scipy.integrate. There I used the vodeintegrator ...
2
votes
1answer
86 views

scipy odeint - Excess work done on this call

I'm newbie both in calculus and Python/Scipy so I apologize if this question is too dumb. I'm trying to model flow between two pressure vessels. Let's say we have two points and a link between them ...
-2
votes
1answer
93 views

Runge-Kutta 4th order for 4 coupled first order differential equation [closed]

I have to solve 4 coupled first order differential equations for $f(t)$ ,$g(t)$, $h(t)$ and $w(t)$ witch are only functions of $t$ , but for every reference link a function of 3 variables is assumed ...
2
votes
1answer
55 views

Solving large, non-linear systems of ODEs numerically: what do I need to consider in order to figure out which solver to use?

I would prefer recommendations that don't require the use of proprietary tools (such as Matlab). I know of two ODE solving options for the Python ecosystem: PyDSTool (Dopri, Radau, other Runge-Kutta ...
0
votes
1answer
25 views

Why might the time taken to compute the solution of an ODE system over some interval increase non-linearly with increasing size of interval?

Currently, my problem requires me to solve a system a large system of non-linear ODEs (up to ~5000). So far, I have been using scipy.integrate.odeint as my ...
1
vote
1answer
20 views

Possible to reduce effort needed to solve non-linear ODEs by taking some coefficients/parameters as constant over small time intervals?

So far, I have been using scipy.integrate.odeint as my "workhorse" ODE solver. My current problem requires that I solve a large system (up to ~5000) ODEs. Here's ...
2
votes
1answer
65 views

How to know whether a boundary-value ODE problem is well defined?

I am using bvp4c from Matlab to solve a boundary values ODEs problem. Given the ODEs and boundary conditions, is there any way to have more information on the solutions? How many do I expect? 0, 1, ...
0
votes
1answer
90 views

scipy.integrate.odeint: how can odeint access a parameter set that is evolving independently of it?

I might have some non-linear ODEs that are being solved by scipy.integrate.odeint. However, a parameter at each time step might have to be updated by using a non-DE ...
1
vote
1answer
50 views

How to impose an integral conservation in solving ODEs boundary value problems (BVP)?

I have a system of coupled ODEs that I want to solve. The functions are A(x), B(x), C(x). It is a boundary values problem. I am using Matlab bvp4c. So far I am not satisfied with my solutions. For ...
2
votes
2answers
153 views

Why does scipy's odeint function give a non-monotonic solution for a problem whose solution should be monotone?

The solution to the ode below looks like it is monotonically increasing: However on closer inspection we see that it is not: How can I ensure that the numerical solution is monotonically ...
6
votes
1answer
75 views

Numerical methods for boundary-value ODEs with a jump condition

I want to solve a non linear system of equations of a particular kind. I find it hard to formulate clearly so I directly give a simple example. $ f''=A(f,g)\\ g''=B(f,g) $ with the boundary ...
6
votes
2answers
434 views

Is the shooting method the only general numerical method for solving nonlinear boundary value ODEs?

During my wandering in Mathematica.se, I gradually noticed that a certain kind of differential equation solving problem is "troubling" us all the time, that is, the boundary value problem (BVP) of ...
3
votes
1answer
189 views

Non-conservative implementation implicit Euler

In Matlab R2013a I have implemented the Implicit Euler (time) integration scheme. To find the $x^{n+1}$ value I use fixed point iterations: $x^{n+1} = \Delta t f(x^{n+1}) + x^n$ To test this, I use ...
4
votes
1answer
97 views

Constructing explicit Runge Kutta methods of order 9 and higher

Some older books I've seen say that the minimum number of stages of an explicit Runge-Kutta method of a specified order is unknown for orders $\geq 9$. Is this still true? What libraries are there ...
3
votes
1answer
66 views

ODE boundary value problem relaxation method reference request

This is a somewhat basic question, I guess. Take the ODE boundary value problem $$ \frac1\lambda y''-y'=0, \qquad y(0) = 0, \quad y(1) = 1, $$ with the solution $$ y(x) = ...
1
vote
1answer
105 views

Solving a system of nonlinear equations with an ODE solver is faster than with the Newton method?

This is somehow unexpected, but my recent experience with solving a system of nonlinear equations is that treating them as the right hand side of a system of ordinary equations and then evolve the ...
1
vote
1answer
52 views

Appropriate algorithm for (non-linear) ODE with integral equilibrium constraint: collocation?

I have a problem of the following structure: For some scalar $g$, functions $F(z)$ and $h(z)$ defined on $[0,\bar{z}]$ , and a non-linear operator $\phi(F,z)$ (in reality, $F$ and $h$ are vector ...
0
votes
2answers
168 views

ode45 solver MATLAB improve time

I am numerically simulating the Mathieu equation using ODE45 and I have to keep changing the parameters delta and epsilon for each simulation to get the required peiodic solution. Following is the ...
1
vote
2answers
179 views

wavelet for numerical partial differential equations

Is there a good introduction into wavelet Galerkin schemes for numerical partial (and ordinary) differential equations?
3
votes
2answers
151 views

scipy odeint: sum of conservative ode equations does not remain zero as it is being solved — is this normal?

Let us say we have the following equations: dy1/dt = f(y1, t) [1] dy2/dt = g(y2, t) [2] The equations are such that they are "conservative", i.e. the ...
1
vote
1answer
72 views

Heuristic help with preconditioning large system ODEs

I'm looking for some general insight on preconditioning. In particular, relevant references/resources/comments would be greatly appreciated. Note, I have been through some of the literature, but am ...
8
votes
2answers
258 views

How to model a fishing rod (or a rope)?

I wish to model a fishing rod (or a rope) by joining short segments. (The segments may have equal (short) length but each segment should be assigned its own individual mass.) One segment will ...
1
vote
2answers
127 views

How to get ODE solution at specified time points?

The code below basically illustrates my problem. It is a test code for a pendulum. I solve it using a method suggested on ...
1
vote
0answers
23 views

Error analysis and the Model Problem [closed]

In numerical methods for ODE's, the model problem y' = cy where c is complex is regarded as sufficient in performing error analysis for different methods in ...
2
votes
1answer
164 views

Adaptive ODE algorithm in Python

I want to integrate a particle path in 2D using the integrate.ode module. Things that are a bit different in my case are that, I only want to integrate up to a ...
0
votes
1answer
104 views

Initial estimate of coupled variables while applying implicit euler to solve nonlinear system of odes

I am trying to solve a system of coupled odes having the following three equations. $$ \begin{align} \frac{dn_A}{dt} & = e\left[j(t) - f\, θ_H\sinh\left(\frac{g\,n_A}{T}\right)\right] \\ ...
5
votes
0answers
100 views

Strategy for solving a non-trivial differential equation

I would like to numerically solve an equation of a type as shown below. Does anyone of you have an idea how to approach such a problem? Any links to literature or for further reading would be greatly ...
3
votes
0answers
30 views

Solving ODE boundary problem with additional conditions

I need to solve two point bondary problem for ODE. The solution of the problem itself is very easy. The real issue is that when solving arising non linear system of equations it always converges to ...
4
votes
2answers
99 views

Solving system of differential equations with interconnected boundary conditions

I am trying to solve the following system of differential equations numerically over the domain $x=0$ to $x=D$. The main difficulty is that the boundary conditions are interconnected and depend on the ...
2
votes
1answer
324 views

Python: Grid with step control ODE solver

I have a problem in physics formulated via an ODE. Now I like to solve it numerically using Pythons scipy.integrate and the therein complex_ode. I figured out how and it works but now I like to ...
3
votes
1answer
261 views

Algorithm for solving an ODE with time-dependent parameter numerically

Would anyone please explain me what is the mathematical algorithm to solve a IVP system of ODE with a time-dependent parameter. e.g. ...
3
votes
1answer
102 views

Options for solving ODE systems on GPUs?

I would like to farm out solving systems of ODEs onto GPUs, in a 'trivially parallelisable' setting. For example, doing a sensitivity analysis with 512 different parameter sets, or solving the ...
2
votes
2answers
505 views

Number of equations and precision of SciPy's integrate.odeint()

Is there any reason why SciPy's integrate.odeint() should become less precise when the number of equations increase? I'm trying to solve these two sets of differential equations: $\frac{dy_1}{dx} = ...
3
votes
3answers
363 views

4th Order Runge-Kutta Method for Coupled Harmonic Oscillator

I'm attempting to write a c program to gather values from a coupled spring system where there is a wall, connected to a mass m1 by a spring, then this mass is connected to a second mass m2 by another ...
5
votes
2answers
143 views

Stability of the first-order exponential integrator method

The question is about the first-order exponential integration method described in this article. Consider a system of ordinary differential equations $$y'(t) = -A\,y(t) + \mathcal{N}(t, y), \qquad ...
6
votes
1answer
361 views

Why am I getting so much error for my Runge Kutta Fehlberg solver?

My current project is a reprogramming of a protein folding model involving the solution of thousands of ODEs in C++. I've been making some stop and start progress as I'm writing the solver to run ...
0
votes
0answers
65 views

Increase convergence of non-linear equations resulting from ODEs

I am trying to solve a set of couple ODEs: $V_l(r) - r W_l(r) - f1(r) W_l' = 0\tag 1$ $r^2 h''_l(r) + f2 r h_l'(r) + f3 h_l(r) - f4 U_l(r) = 0 \tag 2$ $\kappa (U_l + h_l) + V_{l+1} + W_{l+1} = ...
2
votes
2answers
185 views

How can i solve this first order system of differential equations

Edit: I am trying to solve $$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\nu\frac{\partial^{2}u}{\partial x^{2}}\\ u(0,t)=0\nonumber \\ u(1,t)=0\nonumber \\ u(x,0)=\sin(\pi x)\\ ...