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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Nonsmooth dynamic systems simultion using Siconos sofware with Rhenoumous Rheonomous relations [on hold]

I have been working on a nonsmooth dynamic system recently with Siconos software. However, I think I have encountered some problems and I can not find any solutions. My system can be formulated as ...
6
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2answers
370 views

Is the shooting method the only general numerical method for solving nonlinear boundary value ODEs?

During my wandering in Mathematica.se, I gradually noticed that a certain kind of differential equation solving problem is "troubling" us all the time, that is, the boundary value problem (BVP) of ...
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1answer
177 views

Non-conservative implementation implicit Euler

In Matlab R2013a I have implemented the Implicit Euler (time) integration scheme. To find the $x^{n+1}$ value I use fixed point iterations: $x^{n+1} = \Delta t f(x^{n+1}) + x^n$ To test this, I use ...
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1answer
64 views

Constructing explicit Runge Kutta methods of order 9 and higher

Some older books I've seen say that the minimum number of stages of an explicit Runge-Kutta method of a specified order is unknown for orders $\geq 9$. Is this still true? What libraries are there ...
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1answer
58 views

ODE boundary value problem relaxation method reference request

This is a somewhat basic question, I guess. Take the ODE boundary value problem $$ \frac1\lambda y''-y'=0, \qquad y(0) = 0, \quad y(1) = 1, $$ with the solution $$ y(x) = ...
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1answer
84 views

Solving a system of nonlinear equations with an ODE solver is faster than with the Newton method?

This is somehow unexpected, but my recent experience with solving a system of nonlinear equations is that treating them as the right hand side of a system of ordinary equations and then evolve the ...
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1answer
45 views

Appropriate algorithm for (non-linear) ODE with integral equilibrium constraint: collocation?

I have a problem of the following structure: For some scalar $g$, functions $F(z)$ and $h(z)$ defined on $[0,\bar{z}]$ , and a non-linear operator $\phi(F,z)$ (in reality, $F$ and $h$ are vector ...
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2answers
105 views

ode45 solver MATLAB improve time

I am numerically simulating the Mathieu equation using ODE45 and I have to keep changing the parameters delta and epsilon for each simulation to get the required peiodic solution. Following is the ...
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149 views

wavelet for numerical partial differential equations

Is there a good introduction into wavelet Galerkin schemes for numerical partial (and ordinary) differential equations?
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2answers
96 views

scipy odeint: sum of conservative ode equations does not remain zero as it is being solved — is this normal?

Let us say we have the following equations: dy1/dt = f(y1, t) [1] dy2/dt = g(y2, t) [2] The equations are such that they are "conservative", i.e. the ...
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1answer
68 views

Heuristic help with preconditioning large system ODEs

I'm looking for some general insight on preconditioning. In particular, relevant references/resources/comments would be greatly appreciated. Note, I have been through some of the literature, but am ...
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249 views

How to model a fishing rod (or a rope)?

I wish to model a fishing rod (or a rope) by joining short segments. (The segments may have equal (short) length but each segment should be assigned its own individual mass.) One segment will ...
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2answers
108 views

How to get ODE solution at specified time points?

The code below basically illustrates my problem. It is a test code for a pendulum. I solve it using a method suggested on ...
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0answers
20 views

Error analysis and the Model Problem [closed]

In numerical methods for ODE's, the model problem y' = cy where c is complex is regarded as sufficient in performing error analysis for different methods in ...
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1answer
121 views

Adaptive ODE algorithm in Python

I want to integrate a particle path in 2D using the integrate.ode module. Things that are a bit different in my case are that, I only want to integrate up to a ...
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1answer
68 views

Initial estimate of coupled variables while applying implicit euler to solve nonlinear system of odes

I am trying to solve a system of coupled odes having the following three equations. $$ \begin{align} \frac{dn_A}{dt} & = e\left[j(t) - f\, θ_H\sinh\left(\frac{g\,n_A}{T}\right)\right] \\ ...
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96 views

Strategy for solving a non-trivial differential equation

I would like to numerically solve an equation of a type as shown below. Does anyone of you have an idea how to approach such a problem? Any links to literature or for further reading would be greatly ...
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28 views

Solving ODE boundary problem with additional conditions

I need to solve two point bondary problem for ODE. The solution of the problem itself is very easy. The real issue is that when solving arising non linear system of equations it always converges to ...
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2answers
94 views

Solving system of differential equations with interconnected boundary conditions

I am trying to solve the following system of differential equations numerically over the domain $x=0$ to $x=D$. The main difficulty is that the boundary conditions are interconnected and depend on the ...
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1answer
236 views

Python: Grid with step control ODE solver

I have a problem in physics formulated via an ODE. Now I like to solve it numerically using Pythons scipy.integrate and the therein complex_ode. I figured out how and it works but now I like to ...
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1answer
193 views

Algorithm for solving an ODE with time-dependent parameter numerically

Would anyone please explain me what is the mathematical algorithm to solve a IVP system of ODE with a time-dependent parameter. e.g. ...
3
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1answer
97 views

Options for solving ODE systems on GPUs?

I would like to farm out solving systems of ODEs onto GPUs, in a 'trivially parallelisable' setting. For example, doing a sensitivity analysis with 512 different parameter sets, or solving the ...
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2answers
341 views

Number of equations and precision of SciPy's integrate.odeint()

Is there any reason why SciPy's integrate.odeint() should become less precise when the number of equations increase? I'm trying to solve these two sets of differential equations: $\frac{dy_1}{dx} = ...
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3answers
331 views

4th Order Runge-Kutta Method for Coupled Harmonic Oscillator

I'm attempting to write a c program to gather values from a coupled spring system where there is a wall, connected to a mass m1 by a spring, then this mass is connected to a second mass m2 by another ...
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2answers
132 views

Stability of the first-order exponential integrator method

The question is about the first-order exponential integration method described in this article. Consider a system of ordinary differential equations $$y'(t) = -A\,y(t) + \mathcal{N}(t, y), \qquad ...
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1answer
299 views

Why am I getting so much error for my Runge Kutta Fehlberg solver?

My current project is a reprogramming of a protein folding model involving the solution of thousands of ODEs in C++. I've been making some stop and start progress as I'm writing the solver to run ...
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63 views

Increase convergence of non-linear equations resulting from ODEs

I am trying to solve a set of couple ODEs: $V_l(r) - r W_l(r) - f1(r) W_l' = 0\tag 1$ $r^2 h''_l(r) + f2 r h_l'(r) + f3 h_l(r) - f4 U_l(r) = 0 \tag 2$ $\kappa (U_l + h_l) + V_{l+1} + W_{l+1} = ...
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2answers
183 views

How can i solve this first order system of differential equations

Edit: I am trying to solve $$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\nu\frac{\partial^{2}u}{\partial x^{2}}\\ u(0,t)=0\nonumber \\ u(1,t)=0\nonumber \\ u(x,0)=\sin(\pi x)\\ ...
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1answer
135 views

Can the method of lines technique be used to solve a ODE directly for the steady-state value?

Say we have a discretised a coupled nonlinear system of two PDEs to give a system of ODEs which approximates the original system, $$ \frac{\partial u}{\partial t} = F_1(t,\boldsymbol{u,v}) \\ ...
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2answers
161 views

Convert an implicit ODE system to an explicit ODE set to use Runge-Kutta

For my series on mechanical systems with Lagrange, I would like to add the double pendulum and a rolling pendulum. I set up the Lagrangian $L$ and solved for the ODE of motions, and got the following: ...
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1answer
157 views

Numerically solving systems of about 100 ODEs

I am looking to solve large systems of non-linear ODEs. There appears to be a very large list of methods available varying in complexity, and I have a hard time searching through them and picking one. ...
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49 views

Stochastic Collocation for time evolving ODE

For an Stochastic Differential Equation, e.g., $$ \frac{du}{dt} = \alpha*\sin(u*t) $$ where $\alpha$ is normally distributed with nonzero mean, I am trying to use a stochastic collocation approach ...
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1answer
117 views

ode45 usage in this case?

The background is that I'm solving a problem in numerical analysis and I seem to be halfway having solved the non-linear system and now getting to the part where I should apply solving differential ...
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1answer
192 views

Non-linear ordinary differential equation in the modeling of the oscillation of a meniscus

I am trying to model the oscillation of a fluid miniscus in a straw when the miniscus is displaced from its equilibrium level. The results was the following non-linear ODE: $$y''= 1/y - 1.$$ This ...
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2answers
151 views

ODE: How to measure stiffness if the Jacobian has zero eigenvalues?

Say you have a system of ODE's where the Jacobian has one zero eigenvalue; what does that tell you about the stiffness of the system? This case doesn't seem to be discussed in the cases I have been ...
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Energy anomolies in many body simulation

I am trying to simulate the gravitational interaction between many bodies. I am using a direct PP force calculation and a 4th order symplectic integrator with a variable step size. The energy of ...
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610 views

How do I solve a boundary value ODE in MATLAB?

Specifically, ode15i. I have ode15i solving a system of 5 first order implicit odes in 5 variables with an initial condition (made consistent by decic). It's great for what I need, except I need to ...
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2answers
179 views

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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70 views

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

Are there high order energy-conserving or symplectic methods for solving $y'=f(y)$?
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1answer
294 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 ...
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1answer
50 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 ...
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1answer
111 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)] ...
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504 views

What's the state of the art in parallel ODE methods?

I'm currently looking into parallel methods for ODE integration. There is a lot of new and old literature out there describing a wide range of approaches, but I haven't found any recent surveys or ...
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2answers
167 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 ...
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103 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 ...
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185 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 ...
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1answer
80 views

Solving an ODE without a boundary condition [closed]

I have an ODE without a boundary condition: ...
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3answers
626 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 ...
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2answers
335 views

Intermediate values (interpolation) after Runge-Kutta calculation

I have a numerical ODE simulation that I computed at fixed time step $h$ using a 4-th order Runge-Kutta method (RK4), producing a series of results $(x_1,y_1), ...
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4answers
242 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 ...