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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Solve beam equation with elastic term using scipy solve_bvp
I want to solve the beam equation with distributed load and elatic term (which depends on how much the beam interact with the terrain) :
$$
EI\frac{d^4w}{dx^4}+k*(w(x)-t(x))=q(x)
$$
where $q(x)$ is a ...
- 35
5
votes
1
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Time integration of first-order ODE with higher-order information
Suppose I wish to derive a numerical integrator for the first-order ODE $$x'(t)=F(x(t)).$$ By differentiating both sides of the expression in $t$, I can write a second-order relation also satisfied ...
- 1,393
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inverse problem of predicting parameters of ODEs driven by data
Consider a system of ODEs
\begin{align}
u' = f(u,v)\\
v' = g(u,v)
\end{align}
with some unknown parameters in $f$ and $g$, where primes denote time derivatives. No data of $u(t)$ or $v(t)$ are ...
- 317
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2
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Order of numerical solver when calculating difference between forwards and backwards solution
I'm working in applied oceanography, where people are sometimes interested in calculating ``backwards trajectories'' of things floating on the ocean, i.e., going backwards in time to figure out where ...
- 243
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ODEs solved by physics-informed neural networks
Is it possible that an ODE (with an IC) solution by physics informed neural networks (PINNs) turns out to be a mixture of several branch solutions of the same bulk ODE but with different ICs, even ...
- 317
1
vote
1
answer
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Can I combine the backward and forward euler methods - simialr to modified euler method?
Constructing Modified Euler
Using the same strategy as done in the construction of Modified Euler. Starting from Trapezoidal Method
$$y_1 = y_0 + \dfrac{h}{2}\left(f(x_0,y_0) + f(x_1,y_1)\right)$$
...
- 11
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2
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Raman model equations using RK4
I am trying to solve below ODE equations for Raman model but I am having errors, mostly overflow in multiply and add. Please I need your help. Below is the code I have written so far. I am new to ...
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1
answer
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From Runge-Kutta Butcher tableau to general linear methods matrices?
I am trying to understand how the relationship between Butcher tables for Runge-Kutta methods and their generalization to general linear methods matrices (by Butcher also).
Runge-Kutta methods can be ...
- 343
1
vote
1
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Educational Purpose: How to synchronize chaotic systems
The graph plots the X coordinate of the synchronized Lorenz chaotic system. I am self learning by reading research articles on how to synchronize identical chaotic systems. But as seen from the figure,...
- 119
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ode23, 45, 15s, 15i in matlab for conservative ODEs
Which of ode23, 45, 15s, 15i in matlab are dissipative or anti-dissipative for conservative ODEs?
Do they STAY dissipative or anti-dissipative for ALL conservative ODEs nor not? If not, what about for ...
- 317
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shooting method to compute the interface shape
I am trying to use a shooting method to compute the shape of liquid-gas interface given by the following differential equation:
$$
\frac{d^2 \theta}{ds^2} = \frac{f(\theta)}{h(h + 3\lambda)}
$$
with $\...
1
vote
2
answers
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How to estimate the stage error for Runge kutta method
Consider an ordinary differential equation (ODE) in the form $u_t=g(t,u(t))$ and apply the explicit Runge-Kutta method, as defined by the following Butcher tableau:
$$
\mathrm{RK}(s,p):\begin{array}{c|...
- 141
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How to use a custom OdeSolver in Scipy's solve_ivp
In Scipy's solve_ivp documentation, we see the method argument can be either a string or a user-defined ...
- 197
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Local truncation error of given implicit 1-step scheme
I'm given the 1-step implicit scheme $$y_{n+1} = y_n + \frac{h}{6}[4f(t_n, y_n) + 2f(t_{n+1}, y_{n+1}) + hf'(t_n, y_n)],$$
where $y'(t) = f(t, y)$, and I'm seeking the scheme's local truncation error. ...
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Numerical implementation of ODE differs largely from analytical solution
I am trying to solve the ODE of a free fall including air resistance.
I therefore defined my ODE as:
def f(v, g, k, m):
return g - k/m * v**2
which in my ...
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