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

Are there high order energy-conserving or symplectic methods for solving $y'=f(y)$?
1k 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 right-...
953 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 ...
72 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 ...
239 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)] ...
167 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 ...
293 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 ...
3k 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 ...
229 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 ...
326 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 ...
854 views

### How do you improve the accuracy of a finite difference method for finding the eigensystem of a singular linear ODE

I am attempting to solve an equation of the type: $\left( -\tfrac{\partial^2}{\partial x^2} - f\left(x\right) \right) \psi(x) = \lambda \psi(x)$ Where $f(x)$ has a simple pole at $0$, for the ...
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### 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 ...
30 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 ...
213 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 ...
2k 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, ...