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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16 views

Python evaluating a second order ODE with RK4

Pasted below is my python code. It is a 4th order runge kutta that evaluates the 2nd order ode: y'' +4y'+2y=0 with initial conditions y(0)=1, y'(0)=3. I need help fixing it. When I run my code, my ...
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1answer
28 views

Odeint error for nonlineal differential equations

I receive the following error when I run the code. ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information. warnings.warn(...
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73 views

Numerical Issues with DDE from SEIRU$\delta$ model

I'm new in this community. I moved this question from Math community. I'm reading the following article Article Here and my target is to replicate the results for a project. SEIRU Model: I obtained ...
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1answer
78 views

System of moving, non-colliding particles in 1D

I have a system of ODEs for functions $f_i(t)$. At each time $t$, $f_i(t)$ is the position of particle $i$. The functions $f_i$ have a monotonicity property: at all times $0 < f_1(t) < f_2(t) &...
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89 views

Nondifferentiable coordinate transforms

Suppose that we have coordinates $u=u(x,y)$ and $v=v(x,y)$ in $\mathbb{R}^2$ so that $v$ is not differentiable when $u(x,y)=u_0$ where $u_0$ is a constant. Can we solve a differential equation, such ...
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1answer
92 views

Writing a Matlab function after calling the ode45 solver

After using ode45 to solve a set of ODEs, I want to write a Matlab function to take the initial conditions x_0 as inputs and gives the final state x_1 at time T as ...
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82 views

How would one discretize the dynamical equations for Kerr spacetime?

Using the Hamiltonian for a test particle in Kerr spacetime, we arrive at the following equations for generalized position and momenta (in natural units, $G = c = M = 1$): \begin{align} \dot{r} &= ...
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1answer
171 views

Solving Lotka-Volterra Equations on Python

I'm trying to plot Lotka-Volterra Equations using Python. I am a real beginner when it comes to Python. I have these two equations: $$\frac{dR}{dt}=\alpha R-\gamma RF$$ and $$\frac{dF}{dt}=-\beta F+\...
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1answer
113 views

Why is $1/r^2$ force law giving spiral trajectory?

I have written a program to solve for Newton's 2nd Law of motion for a given force law, in 2D polar coordinates. It is known that if the force law is of the form $k/r^2$,we get conic sections as ...
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1answer
83 views

What is a dense ODE system? What is a sparse ODE system?

Can you provide a jargon-free (as much as possible) explanation of what is meant by "dense ODE systems", and "sparse ODE systems"? Some hints I have gotten from Googling: dense ...
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1answer
95 views

Calculating the Strange Attractor of the Duffing Oscillator in C++

I am simultaneously trying to learn computational physics methods, chaos, and C++. I think this is the right site for the question, and I apologise if not. I started working through Thijssen's ...
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65 views

Why is my numerical solution to a set of ODEs infinite?

I am trying to solve the following linear PDEs $$\frac{\partial u_x}{\partial x}=-[i\omega b_{||}+\nabla_\perp u_\perp],$$ $$\frac{\partial b_{||}}{\partial x}=-\frac{i}{\omega}\mathcal{L}u_x,$$ $$\...
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1answer
89 views

ODE forth-order very stiff equation with large errors

I’m using Mathematica home edition software to numerically solve a specific inflation equation in cosmology. The ODE equation is forth- order, non-linear, stiff. I was using the stiffness switching ...
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28 views

Simulating the response of nonlinear system with stiff differential equations

I want to simulate the response of a nonlinear system given in the following form: $$ \dot{x_1} = f_1(\bar{x_1})+g_1(\bar{x_1})x_2, \ x_1(0) = 0.2 $$ $$ \dot{x_2} = f_2(\bar{x_2})+g_2(\bar{x_2})x_3, \...
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1answer
34 views

MATLAB ode45 doesn't start at initial conditions

I wrote a code in MATLAB to solve a system of differential equations, but my solution doesn't seem to take into consideration the initial conditions I specified. I am not sure how to interpret this ...
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3answers
128 views

Runge-Kutta method for an ODE with initial value which is root of denominator

I wrote a code in Fortran to solve this differential equation using RK4 method: $$ \frac{dy}{dx}=A\sqrt{\frac{B}{y}+\frac{C}{y^2}} $$ $A$, $B$, and $C$ are some known constants. The problem is that ...
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1answer
140 views

How can I evaluate more accurate energy eigenvalues from Schrodinger equation using shooting method?

I am trying to use the "shooting method" for solving Schrodinger's equation for a reasonably arbitrary potential in 1D. But the eigenvalues so evaluated in the case of potentials that do not have hard ...
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41 views

Solving a complex ODE with large number of variables (>1e6 variables) - best practise?

I have to solve a non-linear ODE of the shape $$\partial_zA=f(A)$$ with $f$ a non-linear function and $A$ a matrix/vector with >1e6 variables (i.e. $A$ is a matrix with >1000x1000 entries). For each ...
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1answer
120 views

solve_ivp - Overflow encountered in double_scalars

I'm modeling an electron that orbits the nucleus. Of course, charged particles radiate away there energy so it'll crash into the nucleus. My approach has been to to evaluate the coulomb force and add ...
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35 views

Scipy.integrate.odeint is returning curves with almost the same frequency for different damping ratios, shouldn't they be different?

I am trying to solve the ODE for a harmonic oscillator using Scipy's odeint solver for different dampening factors. I'm using the following code, based off of this example: ...
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38 views

More efficient way of solving for transfer function between boundaries of wave equation

I am considering the wave equation with position varying material properties $$ m(x) \frac{\partial^2 u}{\partial t^2} = \frac{\partial}{\partial x}\left(k(x) \frac{\partial u}{\partial x}\right), \...
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39 views

Solving nonlinear pendulum using Runge-Kutta 4 for smaller steps

I am trying to solve nonlinear pendulum using 4th order Runge-Kutta method for limits between a=0.0 to b=110 seconds and simulated the results to observe the pendulum movement. But when I increase the ...
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1answer
192 views

Vectorised second order ode solving in python

I am trying to write a python program that simulates the motion of a large number of particles by numerically integrating a second order ordinary differential equation. I first split the ODE into two ...
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1answer
93 views

Numerical solution of pendulum equation

Given a system of equations: \begin{align} &f''(x) = -a \cdot \sin(f(x))\\ &f(0) = b\\ &f'(0) = c \end{align} $a, b, c, dt, N$ are arbitrary parameters. How to get a values of $f(0), f(...
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71 views

Numerical method for harmonic oscillator with jumping constant

Let $k_1 \neq k_2$ be positive reals, $t_0 > 0$ and consider the following Cauchy problem in $[0,+\infty)$: \begin{cases} y(t) + k(t)y''(t) = 0 \newline y(0) = 1/\sqrt{k_1} \newline y'(0) = 0, \end{...
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1answer
132 views

Solving numerically a linear ODE

I start by saying that I do not have a strong background in numerical analysis, so I may miss some basic things or make trivial mistakes. Motivated by some problems in digital signal processing, I ...
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1answer
187 views

Lambdifying a symbolic matrix in Julia

If I have a symbolic matrix defined as T below, is there any way to lambdify this as function of variables, say σ..., and return ...
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3answers
126 views

Coroutines for ODE solvers

Are there any ODE solver packages that use coroutines and yield their results instead of functions and returning? Briefly, a subroutine in a programming language does some computations, returns a ...
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1answer
63 views

When is a dynamical system discrete vs. continuous?

I have a basic question to ask: Let's say I am reading a paper which gives a good model that consists of a set of ordinary differential equations, with first and second derivatives. Continuity is a ...
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1answer
234 views

integrate.solve_ivp bugged

I am trying to solve an ODE with solve_ivp, but I am getting strange errors. Documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html ...
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1answer
93 views

Solving ODEs with nonlinear constraints

I'm trying to solve an ODE problem. Let's say $\mathbf{x}(t)$ represents the position of a particle at time $t$, and $\mathbf{u}(\mathbf{x},t)$ is a velocity field defined in Cartesian coordinates on ...
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1answer
89 views

Solving a large system of coupled ode. (Python)

I really have a problem here. I have not found a solution yet. The system I need to solve similar to this:(Basic idea) $$c_1 = \dfrac{dx}{dr}+y$$ $$c_2 = \dfrac{dy}{dr}+x$$ Both $c_1/ c_2$ are ...
4
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1answer
244 views

The velocity Verlet method and variable time steps

Does the velocity Verlet handle variable time steps? I found controversial statements about it. In the paper Skeel, R. D., "Variable Step Size Destabilizes the Stömer/Leapfrog/Verlet Method", BIT ...
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1answer
99 views

Numerical integration methods: Explicit vs Semi-Implicit vs Newton-Euler 1, 2 and use in cyclone physics engine

I am trying to understand the difference between explicit Euler and semi-implicit Euler integration, where in explicit Euler the current position is calculated as $$x_{n+1} = x_n + v_n$$ and semi-...
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1answer
76 views

Unexpectedly Slow Convergence Implicit Euler

I'm solving the coupled ODE $$ \left[\begin{array}{c}x^\prime(z)\\p_x^\prime(z)\end{array}\right] = C(z)\cdot\left[\begin{array}{c}x(z)\\p_x(z)\end{array}\right] = \left[\begin{array}{cc}0& A(z)\\...
4
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1answer
97 views

Parareal for particle simulations

Recently I have stumbled upon this video of M. J. Gander https://www.youtube.com/watch?v=dn5vqN8ezuE and the coresponding notes that he wrote on Time Parallel Time Integration and I find it a quite ...
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2answers
205 views

Solving ODE with “Jumpy” Coefficients

I'm numerically solving a linear coupled ODE of the form $$y^{\prime}(t) = \hat{M}(t)y(t)=\left[\begin{array}{cc}0& A(t)\\ B(t)& 0\end{array}\right]y(t),$$ and the difficulty I'm running into ...
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2answers
2k views

Solving coupled differential equations in Python, 2nd order

I have a system of coupled differential equations, one of which is second-order. I am looking for a way to solve them in Python. I would be extremely grateful for any advice on how can I do that! $k$...
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3answers
188 views

Solving coupled ODEs using Runge-Kutta method

I want to solve the following sets of $n$ coupled equations. Initial values of $x_{n}(t)$ and $p_{n}(t)$ are specified. The problem is, I have an 1D lattice where every particle is bound with ...
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0answers
166 views

How to compute numerical fluxes in the local discontinuous galerkin method for poisson equation 1D

Some days ago I began to study the local discontinuous galerkin (LDG) method, this is my first time working with a discontinuous method, so I decided to solve the poisson equation in 1D to learn the ...
2
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1answer
435 views

Numerical Solution to Rayleigh Plesset Equation in Python

I have been trying to numerically solve the Rayleigh-Plesset equation for a sonoluminescence bubble in Python. You can read about this phenomenon here: https://iopscience.iop.org/article/10.1088/0143-...
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2answers
166 views

Solving a 1D diffusion equation with linear and nonlinear source terms

I would like to numerically solve the following equation: $$\frac{\partial \rho (z,t)}{\partial t} = B(N_D \rho (z,t) + \rho(z,t)^2) + D \frac{\partial^2 \rho (z,t)}{\partial z^2}$$ with the boundary ...
3
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1answer
328 views

The Formula of Explicit Runge-Kutta Fourteen order

I need an explicit Runge-Kutta 14th order formula. If you know about some reference that discusses at least 10th order (or higher, since I'm looking for the 14th) of Runge-Kutta and there is ...
4
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1answer
132 views

Recommendation for a fixed-step ODE solver?

My problem involves the solution of a second-order ODE with a fixed-step (input and output). Specifically, this ODE is the radial part of Dirac and Schrödinger equation for a spherical symmetric ...
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0answers
37 views

Can't plot correctly precession of perihelion of Mercury in MATLAB using ode45 or ode23

I was trying to plot precession of perihelion of Mercury using matlab. For this I am following a book Computational Physics by Nicholas J. Giordano and Hisao Nakanishi 2nd Edition. In that book ...
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0answers
20 views

Using nondimensionalization to solve an ode in MATLAB [duplicate]

I am trying to solve an ode that uses some extremely large numbers and some extremely small numbers, namely $$ e = 1.6\times 10^{-19}\\ E = 10^6\\ \tau = 6\times 10^{-24}\\ m = 9.1\times 10^{-31}\\ c ...
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1answer
41 views

How to store all solutions of an ODE on Matlab for multiple values of a parameter

I would like to solve an ODE for multiple values of the parameter p and most importantly, save all the solutions for all the different values. Till now, I have ...
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1answer
117 views

Why is modeling a physical system with ODEs sufficient?

I've read a few papers in dynamical systems where the model equations are sets of ODEs, with the state space, say, the spatial variables x, y, z, and an angle variable phi all evolving forward in time....
2
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1answer
70 views

How to set up a time-dependant matrix for an ODE to be solved using python?

I want to solve a problem numerically in python like this: $$ y(t)' = \mathbf{M}(t)y ,\\ y(0) = (1,0,0,0 ...) $$ where $y$ is an $n$-dimensional vector and $\mathbf{M}(t)$ is a time-dependant $n \...
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1answer
54 views

Attempting to perturb ODE when initial condition is equilibrium point does not work

I have the following system of differential equations: $$ x' = ax- cy + e1 $$ $$y' = by- dx + e2 $$ for variables $x,y$ and parameters $a,b,c,d,e1,e2$. I'd like to solve this in python, which is ...

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