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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63 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
87 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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26 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
33 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
124 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
81 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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40 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
47 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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32 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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22 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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67 views

Solving a non-linear BVP using Finite Differences method

Edit: I have updated my question using the feedback in the comments. I have a boundary value problem that I need to solve using finite difference. My task is specifically to solve it using finite ...
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33 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
100 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
91 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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70 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
128 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
117 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
125 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
56 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
104 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
89 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
73 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 ...
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1answer
187 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
85 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
74 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)\\...
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1answer
93 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
195 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
855 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
169 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
164 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 ...
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1answer
311 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
124 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 ...
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1answer
323 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
121 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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33 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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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
38 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
116 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....
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1answer
66 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
52 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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3answers
150 views

What is the flaw in my stability analysis?

The ODE $${d^2x\over dt^2}=-kx; k>0$$can be converted in the system of linear equations as $$\begin{align} {dx\over dt} & =v\\ {dv\over dt} &= -kx\\ \end{align}$$ Using Euler’s method, ...
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31 views

solving electron motion in undulator by Boris method

I am trying to use Boris scheme to solve the electron trajectory in undulator. The undulator field I used is: $$B_x = b_0\sin(2\pi \tfrac{z}{\lambda_u})$$ where $b_0 = \dfrac{2\pi c_{0}K}{q m_{e} \...
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1answer
64 views

Numerical solution to parametrized second order ODE with nonuniform coefficients

I am trying to solve numerically the following second order linear ODE: $a \frac{\partial^2 u}{\partial x^2} + \frac{\partial u}{\partial x} \frac{\partial a}{\partial x} + b u =0$, on the domain $[...
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1answer
55 views

ODE Event detection for calculating multiple roots of continuous sinusoidal equation

Hey everyone I have a paper that has a method for computing rise and set times of a satellite given a closed form solution. It is a complicated sinusoidal function and the paper has a method to ...
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1answer
84 views

How to Break Coupled ODEs down to first order for Runge-Kutta

My question might seem a bit simple. I am trying to solve a system of ODEs using Runge-Kutta method. I am having difficulty breaking down the equations into a system of first order ones required ...
2
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1answer
53 views

Passing data as arguments in ODE45

I need to import data from file in order to describe the structure of a network. I used the following: weights = readtable('weights192.txt'); W = weights{:,:}; ...
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2answers
111 views

ode45 with matrix initial conditions

EDIT: We have a coupled system of 10 ode each. The coupling presents in the last equation. I thought about using a matrix 10 by 2 as initial conditions. I also followed a similar question with the ...
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1answer
128 views

Eigenvalue-like problem with coupled ODEs

I am looking at the following system of ODEs: \begin{array}{r}{\left[c_{2}(k)-\partial_{\tau}^{2}\right] \varphi_{2}\left(\tau \right)=f_{21}(\tau) \varphi_{1}\left(\tau \right)} \\ {\left[c_{1}(k)-...
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0answers
39 views

Equivalent of multiple-scale analysis for a linear ODE

I came across the method of multiple-scale analysis and was intrigued, because I am trying to solve a linear ODE with multiple characteristic timescales. When I apply the method as described, say, ...
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59 views

How to deal with a huge system of ODEs in Boost ODEINT?

I am using the C++ library ODEint, which is part of Boost, to solve an extremely large system of coupled ODEs - in particular 1975 equations with large rational functions in the coefficients. In the ...

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