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.

Filter by
Sorted by
Tagged with
0
votes
1answer
24 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 ...
-1
votes
0answers
46 views

Solving ODE for Mosquito Densities

I am trying to calculate the densities of mosquitoes at different life cycle stages. I want to use historical weather data (such as air and water temperature) and compare the results of the model to ...
2
votes
1answer
76 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 ...
-1
votes
1answer
62 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 ...
-1
votes
0answers
35 views

Solving a 2-time Volterra integro-differential equation

In non-equilibrium field theory one usually encounters the so called Kadanoff-Baym equations, which are Volterra integro-differential of 2 times $$ i \partial_t f(t,t^\prime) = h(t) f(t, t^\prime) + \...
4
votes
1answer
158 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 ...
1
vote
1answer
69 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-...
1
vote
1answer
67 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
votes
1answer
85 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 ...
3
votes
2answers
178 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 ...
4
votes
1answer
156 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! $k$...
-1
votes
3answers
153 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 ...
4
votes
0answers
153 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
votes
1answer
126 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-...
1
vote
2answers
84 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
votes
1answer
319 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
votes
1answer
113 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 ...
0
votes
0answers
29 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 ...
1
vote
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 ...
2
votes
1answer
35 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 ...
0
votes
1answer
112 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
votes
1answer
58 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 \...
1
vote
1answer
48 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 ...
2
votes
3answers
140 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, ...
0
votes
0answers
29 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} \...
2
votes
1answer
62 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 $[...
1
vote
1answer
50 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 ...
1
vote
1answer
75 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
votes
1answer
50 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{:,:}; ...
3
votes
2answers
95 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 ...
8
votes
1answer
124 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)-...
2
votes
0answers
37 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, ...
1
vote
0answers
51 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 ...
0
votes
0answers
32 views

Solutions in Ngspice do not converge to right value

I recently noticed while using Ngspice that the solution converges to a deviated value if the number of iterations per unit period for a square wave is less than 100, i.e. if I am using a square wave ...
3
votes
1answer
81 views

Good reference on the implementation and limitations of SDIRK methods

For the solution of many PDE, implicit high-order time integration schemes are required. I am specifically interested in schemes that do not require a constant time step. I am well acquainted with ...
0
votes
0answers
52 views

A non linear ode with boundary conditions at infinity

I want to solve the non-linear ODE $$\frac{d^2}{dx^2}y=a(y+y^3)$$ With the boundary conditions that $$\lim_{x\to \pm \infty} y(x) =0$$ I am not aware of any analytical method for solving this kind ...
2
votes
0answers
49 views

Can Taylor methods be used effectively on stiff ODEs?

Cleve Moler has stated that "all numerical methods for stiff odes are implicit." However, I don't know whether this statement is a mathematical fact, or an simply an observation. Moreover, many ...
2
votes
0answers
67 views

How to solve $y(x) y'''(x)=f(x)$

I have a PDE of the form $\partial_t y(x,t)+\partial_x(y(x) y'''(x)-f(x))=0$, where $f(x)=\cos(x)$. Suppose a stable equilibrium exists, and I want to find the steady-state solution $y(x) y'''(x)=f(x)...
15
votes
5answers
1k views

Why does the numerical solution of an ODE move away from an unstable equilibrium?

I wish to simulate the behaviour of a double-pendulum-like system. The system is a 2-degrees-of-freedom robot manipulator that is not actuated and will, therefore, behave mostly like a double-pendulum ...
6
votes
1answer
91 views

Going back in time in an initial value problem

Consider an initial value problem (IVP) $y'=f(t,y)$ with the initial value given by $y(t=0) = 0$. If I need to find $y(t^*)$, hence finding the path for $y$ in $t \in [0,t^*]$ and $t^*<0$; is the ...
5
votes
1answer
95 views

What are systematic ways of approximating a non-smooth (non-continuously differentiable) system dynamic to be n-smooth?

I have a system dynamic that is non-smooth because it has several signum and absolute value functions in it (three-tank level control). I can obviously choose different sigmoid functions to ...
4
votes
1answer
92 views

$L^\infty$ stability property of an ODE

Suppose we have the initial-value problem on $(0,L)$: $$ \frac{d u(x)}{d x} = f(x) u(x),\, \qquad x\in\Omega,\,~~ u(0) = u_0, $$ I am reading a claim that says if we multiply the ODE by $u$ and ...
2
votes
1answer
62 views

Symplectic linear multistep method?

I'm doing a gravitational n-body simulator and I'm thinking of implementing linear multistep methods like Adam-Bashforth. But is there any symplectic multistep methods?
0
votes
0answers
47 views

Computing Trajectory Equations of Kerr Geodesics

I want to numerically solve the trajectory equations of a Kerr geodesic given by wikipedia in Matlab. The trajectories look like: I implemented the equations and solved it with the standard Runge-...
2
votes
1answer
298 views

Forward and backward integration — cause of errors

I write a test program to integrate foward on $[0,T_f]$ and then backward on $[T_f,0]$ from the endpoint of the forward integration an Hamiltonian system: $$ \dot q(t) = \frac{\partial H}{\partial p}(...
0
votes
0answers
27 views

Finding the polynomial for the solution of an ODE

I’m stuck trying to solve part (b) and (c) of the below problem, but part (b) is the one of main concern here as I think (c) should follow easily once (b) is completed. I don’t know where to start ...
1
vote
0answers
46 views

Finite dimensional optimization problem over dynamical system

I am interested in solving numerically the following mathematical problem Consider an ode of the form $$ \dot q(t) = f(q(t),t_1,\ldots, t_N),\qquad t\in [0,T], $$ where $q\in \mathbb{R}^n$ is the ...
7
votes
1answer
169 views

Is there any explicit symplectic Runge-Kutta method?

As far as I know, all the symplectic Runge-Kutta methods are implicit which need to solve non-linear equations during the calculation. Is there any explicit method? If not, why?
1
vote
1answer
67 views

Online Parameter Estimation using steepest descent

I have a first order system which is described by the following differential equation: dx/dt = -a*x + b*u where u is the input <...
2
votes
1answer
38 views

Discretization with non-constant matrix containg entries form unknown vector

Consider a system of PDEs $$ \begin{cases} u_t = \nabla \cdot (D(u)\nabla u) + \frac{c}{K_U+c}u-ku\\ c_t = d_c\Delta c -\frac{\nu_U c}{K_U + c}u \end{cases} $$ with some boundary conditions. Here, $D(...

1
2 3 4 5
8