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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2
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1answer
69 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
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1answer
42 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
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0answers
88 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
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0answers
25 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
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2answers
78 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
108 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
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1answer
117 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
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1answer
88 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
125 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
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3answers
286 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 ...
3
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0answers
74 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
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1answer
227 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
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0answers
57 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
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2answers
176 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)\\ ...
0
votes
1answer
104 views

Can the method of lines technique be used to solve a ODE directly for the steady-state value?

Say we have a discretised a coupled nonlinear system of two PDEs to give a system of ODEs which approximates the original system, $$ \frac{\partial u}{\partial t} = F_1(t,\boldsymbol{u,v}) \\ ...
4
votes
2answers
136 views

Convert an implicit ODE system to an explicit ODE set to use Runge-Kutta

For my series on mechanical systems with Lagrange, I would like to add the double pendulum and a rolling pendulum. I set up the Lagrangian $L$ and solved for the ODE of motions, and got the following: ...
6
votes
1answer
146 views

Numerically solving systems of about 100 ODEs

I am looking to solve large systems of non-linear ODEs. There appears to be a very large list of methods available varying in complexity, and I have a hard time searching through them and picking one. ...
3
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0answers
45 views

Stochastic Collocation for time evolving ODE

For an Stochastic Differential Equation, e.g., $$ \frac{du}{dt} = \alpha*\sin(u*t) $$ where $\alpha$ is normally distributed with nonzero mean, I am trying to use a stochastic collocation approach ...
2
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1answer
111 views

ode45 usage in this case?

The background is that I'm solving a problem in numerical analysis and I seem to be halfway having solved the non-linear system and now getting to the part where I should apply solving differential ...
3
votes
1answer
186 views

Non-linear ordinary differential equation in the modeling of the oscillation of a meniscus

I am trying to model the oscillation of a fluid miniscus in a straw when the miniscus is displaced from its equilibrium level. The results was the following non-linear ODE: $$y''= 1/y - 1.$$ This ...
5
votes
2answers
131 views

ODE: How to measure stiffness if the Jacobian has zero eigenvalues?

Say you have a system of ODE's where the Jacobian has one zero eigenvalue; what does that tell you about the stiffness of the system? This case doesn't seem to be discussed in the cases I have been ...
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0answers
43 views

Energy anomolies in many body simulation

I am trying to simulate the gravitational interaction between many bodies. I am using a direct PP force calculation and a 4th order symplectic integrator with a variable step size. The energy of ...
5
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2answers
397 views

How do I solve a boundary value ODE in MATLAB?

Specifically, ode15i. I have ode15i solving a system of 5 first order implicit odes in 5 variables with an initial condition (made consistent by decic). It's great for what I need, except I need to ...
3
votes
2answers
147 views

How to decide stability of Runge-Kutta method for non-linear ODE?

I'm working on a parameter study of Duffing's equation $\ddot x + \delta \dot x + \alpha x + \beta x^3 = \gamma \cos{\omega t},$ where $\delta, \alpha, \beta, \gamma$ and $\omega$ are real ...
6
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1answer
67 views

Are there high order symplectic methods for $y'=f(y)$?

Are there high order energy-conserving or symplectic methods for solving $y'=f(y)$?
5
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1answer
259 views

Code to numerically integrate a system of first-order ODEs

I need to solve the following system of differential equations. When I have the solutions for $n_f$ and $v$, I need to find and plot $J=-e_\cdot n_{f} \cdot v$. I wrote a code in matlab with all ...
1
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1answer
48 views

Can you give me a detailed description of (spetral) deferred correction method?

I have just read "Accelerating the convergence of spectral deferred correction methods". The link is here: http://www.unc.edu/~junjia/papers/sdcgmres.pdf‎. But I wonder how to understand deferred ...
1
vote
1answer
100 views

ODE Solving in SCILAB

I have a certain ODE problem which needs to be solved using Scilab. dx(1)/dt=k*x(1)-x(5) dx(2)/dt=k2*x(2)-k1*x(1) dx(3)/dt=k1*[x(2)-x(3)] dx(4)/dt=k1*[x(3)-x(4)] ...
24
votes
2answers
401 views

What's the state of the art in parallel ODE methods?

I'm currently looking into parallel methods for ODE integration. There is a lot of new and old literature out there describing a wide range of approaches, but I haven't found any recent surveys or ...
2
votes
2answers
150 views

Nanoseconds vs. picoseconds in numerical quantum problems with Matlab ODEs

Hello there and thanks for taking a look at this problem. This problem is related to my previous question and I will therefore use a similar introduction from, Choice of step size using ODEs in ...
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0answers
93 views

Block Backward Differentiation Formula (BBDF), on order 4 formula

I am trying to implement a program the numerical method to solve ODE called Block BDF as explained in this article: https://waset.org/journals/waset/v38/v38-49.pdf As it is variable step-size, I need ...
3
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1answer
179 views

Heat transfer in pipe

I have a gas (assuming air) at $T$ = 500 K that enters a cylindrical pipe. The outlet target temperature is 330 K. There will be heat transfer via: Forced convection from the gas to the inside of the ...
1
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1answer
80 views

Solving an ODE without a boundary condition [closed]

I have an ODE without a boundary condition: ...
9
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3answers
397 views

Choice of step size using ODEs in matlab

Hey there and thanks for giving time to look at my question. This is a updated version of my question which I posted earlier in physics.stackexchange.com I'm currently studying a 2D exciton spinor ...
4
votes
2answers
269 views

Intermediate values (interpolation) after Runge-Kutta calculation

I have a numerical ODE simulation that I computed at fixed time step $h$ using a 4-th order Runge-Kutta method (RK4), producing a series of results $(x_1,y_1), ...
13
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4answers
222 views

Optimal ODE method for fixed number of RHS evaluations

In practice, the runtime of numerically solving an IVP $$ \dot{x}(t) = f(t, x(t)) \quad \text{ for } t \in [t_0, t_1] $$ $$ x(t_0) = x_0 $$ is often dominated by the duration of evaluating the ...
0
votes
1answer
96 views

Spring damper model does not work very well

I'm trying to model a spring damper system from a tutorial that I've found on this site. If I use the exact same parameters as the ones in the tutorial the system is not stable. I've downloaded the ...
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0answers
18 views

Combining trend estimation and constrained Marquart fit

This title certainly needs some clarification: I need to compute parameters $a_i$ for a helper function $f(\vec{a};k)$ (for grid interpolation) which is fitted to a number of values $y_k$ which are ...
4
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1answer
155 views

Solving Coupled ODE eigenvalue problem

I've been trying to find some resources that would help me figure out how to numerically solve a coupled system of ODEs which is also an eigenvalue problem. The system is something like: $ \tag{1} ...
21
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3answers
382 views

How does one test a numerical ODE solver implementation?

I'm about to start working on a software library of numerical ODE solvers, and I'm struggling with how to formulate tests for the solver implementations. My ambition is that the library, eventually, ...
3
votes
2answers
73 views

Best form for a system of ODEs to solve with Runge_kutta

Recently when I was solving a system of ODEs using runge-Kutta method , I got much different results when I transformed the variables from spherical coordinates ($r$ and $\theta$ ) to cylindrical ...
3
votes
1answer
606 views

4th order Padé scheme formula derivation

I am trying to derive the formula of the 4th order Padé scheme that passes through the points $x_i$, $x_{i-1}$ and $x_{i+1}$ $$\Big(\frac{\partial\phi}{\partial x} \Big)_i = ...
1
vote
2answers
374 views

Solver error in SciPy/LSODA with a very specific parameter set

I'm implementing a very simple Susceptible-Infected-Recovered model with a steady population for an idle side project - normally a pretty trivial task. But I'm running into solver errors using either ...
8
votes
4answers
231 views

Reference request: Rigorous analysis of algorithms for PDE and ODE

I'm interested in suggestions for book references on the subject of numerical PDE and ODE, in particular, a rigorous analysis of such methods in a manner written for professional mathematicians. It ...
7
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3answers
208 views

Numerically stable explicit solution of small linear system

I have an inhomogeneous linear system $$ Ax=b $$ where $A$ is a real $n\times n$ matrix with $n\leq 4$. The nullspace of $A$ is guaranteed to be of zero dimension so the equation has a unique ...
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0answers
103 views

Memory errors with GSL ODE solver

I am trying to solve a (large) system of ODEs with GSL solvers. When I use driver method I get an error message of could not allocate space for gsl_interp_accel, ...
3
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0answers
51 views

Dissipation and symplectic manifolds

I'm working on an API for simulation of port-Hamiltonian systems. As far as I understand it, a Hamiltonian system is symplectic if it is power conserving, and so including resistive elements would ...
5
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1answer
86 views

Modern alternatives to DRESOL Riccati solver

I am looking for a modern version or an alternative to the DRESOL package for differential matrix Riccati equations. The main issue that the original package uses single-precision type ...
6
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2answers
108 views

numerical investigation of stability of motion (confinement)

I am trying to find the required specifications of a RF trap, in which a proton can be confined.(trap dimensions,voltage frequency and amplitude used, etc). I have to solve the equations of motion ...
5
votes
3answers
182 views

Is there a way to reduce aberration in computations of planets' trajectories?

I don't think the title is very accurate , sorry for that. I simulate bodies in space using two timestep: the TIMESTEP is the Δt wich I use to make the calculation and XTIME is the number of times ...