# Questions tagged [time-integration]

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### Boundary condtions on nonlinear FEM time integration

I'm using the finite element method to obtain the time response of a structure harmonically excited. I'm using a linear displacement function to obtain the stiffness matrix and the consistent mass ...
2k views

### Why is leapfrog integration symplectic and RK4 not, if the latter is more accurate?

In a system where energy theoretically should be conserved, the most accurate simulation would conserve energy (as well as giving accurate positions, velocities and etc). RK4 is more accurate than ...
253 views

### Solving a differential equation using numerical methods and matlab

(a) Consider the following differential Equation $$Y'(t)=\frac{1}{1+t^{2}}-2[Y(t)]^2$$ $$Y(0)=0$$ The exact solution is $$Y(t)=\frac{t}{1+t^2}$$ Using the Euler method to solve the following ...
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### Time integration for elastodynamics

I'd like to solve the elastodynamics equation for a problem with fast scales from an impact (although no shocks). $\rho\ddot{\mathbf{u}} - \nabla \cdot \sigma(\mathbf{u}) = \mathbf{f}$ In structural ...
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149 views

### How does Multi Body Dynamics software work for flexible joints?

I need to model a "fishing rod" in 2 dimensions by joining several "rigid sticks" by flexible/elastic joints. The joints act as plate/torsion springs with different spring constants. The "fishing rod" ...
327 views

### Computational time not proportional to integration interval in ODE-solver?

I am running octave and i have been trying ode45, ode54, ode23 etc to integrate the equation  $$Q''(t) = B\cos(Q)\sin(\omega t)$$ $$Q(t=0)=0.$$ When the time interval to be integrated increases, the ...
55 views

### Second and Higher Order Order Corrector in Spectral Deferred Correction

I am trying to work out a second order or higher order correction for the method of Spectral deferred Correction (SDC). Specifically using as a corrector a second order or third order multi-step. In ...
2k views

### Time step size for transient simulations of vortex shedding

I am simulating unsteady flow around a circular cylinder (using FLUENT). I am facing the following problem. Kindly please help me. OBJECTIVE: To find out the Reynolds number at which vortex shedding ...
530 views

### Fourth order IMEX Runge-Kutta method

I am looking for the Butcher tableau of a fourth order accurate Runge-Kutta method with IMEX splitting. I have been reading the ''classical'' paper on the subject by Ascher, Ruuth and Spiteri as well ...
131 views

### Why do planets move at the wrong speed in my solar system model?

Not 100% sure where this question belongs, since I'm not sure if the problem is code related or not. I've written a program to model the solar system. I am now testing its accuracy. I've checked ...
938 views

### Which numerical methods preserve time reversal symmetry?

If I have a physical system which contains a time reversal symmetry (for example a Hamiltonian $H(x,p)=p^2/2m + V(x)$ with $V(x)$ real) and I want to solve the differential equations which describe ...
176 views

### Is it worth switching to timesteppers provided by PETSc if I can't write down a Jacobian for my problem? Case study with “the amoeba” toy problem

I am considering using petsc4py instead of scipy.integrate.odeint (which is a wrapper for Fortran solvers) for a problem ...
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### Why not solve molecular dynamics trajectories exactly?

The basis of Molecular Dynamics simulation is the integration of newton's equations of motion: $$\frac{F}{m} = \frac{d^2r}{dt^2}$$ I understand that there are various methods based on Taylor's ...
573 views

### Time discretization of wave equation

I am trying to model the seismic wave equation and have therefore been reading about discretization schemes and their stability. I recently came across an insightful paper on 'Galerkin FEM methods for ...
563 views

### BDF methods for implicit-explicit method

Are there BDF formulas like the ones given here but one that can be used with implicit-explicit discretization? The right hand side in those formulas is supposed to be implicitly discretized at the ...
366 views

### How to physically understand time dependent boundary conditions?

I am a beginner in Computational science and FEM. I came across some PDEs which implement time dependent boundary conditions. I am not able to visualize exactly a physical scenario of how that would ...
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### PDEs appropriate for adaptive time stepping algorithms

I'm looking for some physical phenomena for which an adaptive time stepping algorithm would be ideal. A PDE or ODE that showed very large gradients in time at a small period of time and smoother ...
47 views

### comparison of stability of two non-linear methods

I have solved a numerical problem using two different sets of non-linear governing equations. I want to get an understanding of the stability of the methods relative to each other. To do so, I solving ...
891 views