# 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 implement adaptive step size Runge-Kutta Cash-Karp?

Trying to implement an adaptive step size Runge-Kutta Cash-Karp but failing with this error: ...
84 views

### Solving an ODE from many starting points

I have a situation where I'm interested in solving the same ODE many times, from different initial locations. More precisely, I'm interested in solving an ODE of the form \begin{align} \frac{dx}{dt} &...
68 views

### Finite differenced eigenvalue prob. of inhomogeneous boundary conditions?

I am basically asking about eigenvalue problems of differential equations using some finite difference method (FDM). Usually the system is subject to some boundary conditions (BC), e.g., Dirichlet or ...
1k views

### Using RK2 Method to solve the simple harmonic oscillator of a horizontal mass on a spring (1D)

Being new to numerical analysis techniques, in particular RK2, I decided the best way to jump in is by using python to solve the well known mass-spring oscillator using RK2 techniques. My problem is ...
554 views

### Scaling step size in adaptive runge-kutta method

I'm developing my own generic Runge-Kutta solver, and I'm currently implementing the adaptive step-size routine. I say generic because I want to be able to test different RK implementations by only ...
151 views

### How to obtain the reduced model from a subspace projection method?

I have a system of ordinary differential equations (ODEs). It is a large system that has dozens of equations and hundreds of parameters. I wish to reduce its size so it becomes computationally more ...
232 views

### ODE events to switch between 5 equations (friction model)

I am modelling a 1 dof spring-mass-damper system with friction. As first attempt I modelled the friction according to the simple Coulomb model (figure A here http://article.sapub.org/image/10.5923.j....
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### Stiffness emerges as number of ODEs increases

I want to solve a system of ordinary differential equations with Matlab. I need this to solve a mechanical engineering related problem. If $n$ is the number of degrees of freedom of my mechanical ...
I want to solve a system of coupled nonlinear 1-D PDE $(\partial_{tt} + \alpha\partial_t)u_i(x,t)=\partial_{xx}(\sum_{j=1}^{j<i}ju_j(x,t)+i\sum_{j=i}^{n}u_j(x,t))-\sin(u_i(x,t))+f$, using method of ...